Maths-
General
Easy

Question

The equation of tangent to the ellipse x2 + 3y2 = 3 which is perpendicularr to line 4y = x – 5 is-

  1. 4x + y + 7 = 0    
  2. 4x + y – 7 = 0    
  3. 4x + y – 3 = 0    
  4. None of these    

hintHint:

find out the slope of the tangent and substitute the value of m into the equation of tangent of an ellipse.

The correct answer is: 4x + y + 7 = 0



    y+ 4x ± 7=0
    slope of given line : 1/4
    slope of line perpendicular to this : -4

    equation of ellipse: 4x2/5+3y2/5=1
    here , a2= 3, b2= 1
    equation of tangent of an ellipse : y= mx ± √(a2m2+b2)

    y=-4x± √(3(16) +1)
    y=-4x ± 7
    y+ 4x ± 7=0

    slope of parallel lines are equal and product of perpendicular lines is -1.
    this can be used to find the required slope.

    Related Questions to study

    General
    Maths-

    The equation of the tangents to the ellipse 4x2 + 3y2 = 5 which are parallel to the line y = 3x + 7 are

    parallel lines have exactly equal slopes and perpendicular lines have the product of their slopes =-1. from this, we can find out the slope of the tangent of the ellipse.

    The equation of the tangents to the ellipse 4x2 + 3y2 = 5 which are parallel to the line y = 3x + 7 are

    Maths-General

    parallel lines have exactly equal slopes and perpendicular lines have the product of their slopes =-1. from this, we can find out the slope of the tangent of the ellipse.

    General
    Maths-

    The ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction+ fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction = 1 and the straight line y = mx + c intersect in real points only if-

    since the curves intersect at real points only, D should be greater than 0

    The ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction+ fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction = 1 and the straight line y = mx + c intersect in real points only if-

    Maths-General

    since the curves intersect at real points only, D should be greater than 0

    General
    Maths-

    The line x cos alpha + y sin alpha = p will be a tangent to the conic fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction+ fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction= 1, if-

    the tangent touches the curve at a single point and hence, has a single real solution to the equation.

    The line x cos alpha + y sin alpha = p will be a tangent to the conic fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction+ fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction= 1, if-

    Maths-General

    the tangent touches the curve at a single point and hence, has a single real solution to the equation.

    parallel
    General
    Maths-

    Find the equations of tangents to the ellipse 9x2 + 16y2 = 144 which pass through the point (2,3).

    equation of tangent of an ellipse is given by :
    y= m+ √(a2m2+b2)
    this is used to find the values of m.

    Find the equations of tangents to the ellipse 9x2 + 16y2 = 144 which pass through the point (2,3).

    Maths-General

    equation of tangent of an ellipse is given by :
    y= m+ √(a2m2+b2)
    this is used to find the values of m.

    General
    Maths-

    Find the equation of the tangent to the ellipse x2 + 2y2 = 4 at the points where ordinate is 1.

    the standard form of equation of tangents is obtained by substituting the values of coordinates into the equation of the curve

    Find the equation of the tangent to the ellipse x2 + 2y2 = 4 at the points where ordinate is 1.

    Maths-General

    the standard form of equation of tangents is obtained by substituting the values of coordinates into the equation of the curve

    General
    Maths-

    If fraction numerator x over denominator a end fraction+ fraction numerator y over denominator b end fraction = square root of 2 touches the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction+ fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction= 1, then its eccentric angle θ is equal to-

    the standard equation of an ellipse is obtained by substituting the parametric point on the curve equation.

    If fraction numerator x over denominator a end fraction+ fraction numerator y over denominator b end fraction = square root of 2 touches the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction+ fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction= 1, then its eccentric angle θ is equal to-

    Maths-General

    the standard equation of an ellipse is obtained by substituting the parametric point on the curve equation.

    parallel
    General
    Maths-

    The position of the point (4,– 3) with respect to the ellipse 2x2 + 5y2 = 20 is-

    the position of a point with respect to a curve can be calculated by substituting the point and finding the resultant value
    if it is less than zero,  then it lies inside the curve
    equal to zero  then lies on the curve
    greater than zero then lies outside the curve

    The position of the point (4,– 3) with respect to the ellipse 2x2 + 5y2 = 20 is-

    Maths-General

    the position of a point with respect to a curve can be calculated by substituting the point and finding the resultant value
    if it is less than zero,  then it lies inside the curve
    equal to zero  then lies on the curve
    greater than zero then lies outside the curve

    General
    Maths-

    The parametric representation of a point on the ellipse whose foci are (– 1, 0) and (7,0) and eccentricity 1/2 is-

    the parametric form of a point on the ellipse gives us the coordinates of any point on the ellipse for a given angle.

    The parametric representation of a point on the ellipse whose foci are (– 1, 0) and (7,0) and eccentricity 1/2 is-

    Maths-General

    the parametric form of a point on the ellipse gives us the coordinates of any point on the ellipse for a given angle.

    General
    Maths-

    Let P be a variable point on the ellipse fraction numerator x to the power of 2 end exponent over denominator 25 end fraction + fraction numerator y to the power of 2 end exponent over denominator 16 end fraction =1 with foci S and S'. If A be the area of triangle pss', then maximum value of A is–

    the maxima or minima of a function is calculated by finding out the critical points of the function and then substituting the value of the critical point in the function.

    Let P be a variable point on the ellipse fraction numerator x to the power of 2 end exponent over denominator 25 end fraction + fraction numerator y to the power of 2 end exponent over denominator 16 end fraction =1 with foci S and S'. If A be the area of triangle pss', then maximum value of A is–

    Maths-General

    the maxima or minima of a function is calculated by finding out the critical points of the function and then substituting the value of the critical point in the function.

    parallel
    General
    Maths-

    If S and S' are two foci of an ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction + fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction = 1 (a < b) and P (x1, y1) a point on it, then SP + S' P is equal to-

    the length of major axis of an ellipse is 2a for a horizontal ellipse and 2b for a vertical ellipse. a horizontal ellipse is formed when a>b and a vertical ellipse is formed when b>a. the major axis lies along x axis when a>b and along y axis when b>a.

    If S and S' are two foci of an ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction + fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction = 1 (a < b) and P (x1, y1) a point on it, then SP + S' P is equal to-

    Maths-General

    the length of major axis of an ellipse is 2a for a horizontal ellipse and 2b for a vertical ellipse. a horizontal ellipse is formed when a>b and a vertical ellipse is formed when b>a. the major axis lies along x axis when a>b and along y axis when b>a.

    General
    Maths-

    The eccentricity of the ellipse represented by the equation 25x2 + 16y2 – 150x – 175 = 0 is -

    the given equation has to be converted into the whole square form for x and y so that the standard form of ellipse can be observed. from the standard form, the eccentricity can be calculated by the values of a and b.

    The eccentricity of the ellipse represented by the equation 25x2 + 16y2 – 150x – 175 = 0 is -

    Maths-General

    the given equation has to be converted into the whole square form for x and y so that the standard form of ellipse can be observed. from the standard form, the eccentricity can be calculated by the values of a and b.

    General
    Maths-

    The foci of the ellipse,25 (x + 1)2 + 9 (y + 2)2 = 225, are at-

    the ellipse has its vertex at (-1,-2). The terms x+1 and y+2 can be replaced with X and Y for better understanding so that it gets converted into the standard form.

    The foci of the ellipse,25 (x + 1)2 + 9 (y + 2)2 = 225, are at-

    Maths-General

    the ellipse has its vertex at (-1,-2). The terms x+1 and y+2 can be replaced with X and Y for better understanding so that it gets converted into the standard form.

    parallel
    General
    Maths-

    The equation of the ellipse whose one of the vertices is (0, 7) and the corresponding directrix is y = 12, is-

    this form of ellipse is a vertical one,i.e., the y axis is the major axis and the x axis is the minor axis.

    The equation of the ellipse whose one of the vertices is (0, 7) and the corresponding directrix is y = 12, is-

    Maths-General

    this form of ellipse is a vertical one,i.e., the y axis is the major axis and the x axis is the minor axis.

    General
    Maths-

    The equation of ellipse whose distance between the foci is equal to 8 and distance between the directrix is 18, is-

    the focii are located at (ae,0) and (-ae,0). the distance between them is (ae-(-ae))= 2ae
    similarly, the directrices are at a/e and -a/e .

    The equation of ellipse whose distance between the foci is equal to 8 and distance between the directrix is 18, is-

    Maths-General

    the focii are located at (ae,0) and (-ae,0). the distance between them is (ae-(-ae))= 2ae
    similarly, the directrices are at a/e and -a/e .

    General
    chemistry-

    Ionizatioenergieofive elements in kcal/moargivebelow:

    The element having most stable oxidation state +2 is ?

    Ionizatioenergieofive elements in kcal/moargivebelow:

    The element having most stable oxidation state +2 is ?

    chemistry-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.