Question
The locus of the point of intersection of the perpendicular tangents to the ellipse 
+ 
= 1 is
- x2 + y2 = 9
- x2 + y2 = 4
- x2 + y2 = 13
- x2 + y2 = 5
Hint:
find the equation of director circle
The correct answer is: x2 + y2 = 13
x2+y2= 13
perpendicular tangents are drawn from the director circle
equation of director circle :
x2+y2= a2+b2
x2+y2= 9+4=13
x2+y2= 13
perpendicular tangents are drawn from the director circle
Related Questions to study
From the point (
, 3) tangents are drawn to + = 1 and are perpendicular to each other then =
perpendicular tangents are drawn from the director circle
From the point (, 3) tangents are drawn to + = 1 and are perpendicular to each other then =
perpendicular tangents are drawn from the director circle
Two perpendicular tangents drawn to the ellipse
+ 
= 1 intersect on the curve -
the tangents drawn from the director circle intersect at right angle.
Two perpendicular tangents drawn to the ellipse + = 1 intersect on the curve -
the tangents drawn from the director circle intersect at right angle.
The angle between the pair of tangents drawn to the ellipse 3x2+ 2y2 = 5 from the point (1,2) is-
use the equation of S to find the value of theta.
The angle between the pair of tangents drawn to the ellipse 3x2+ 2y2 = 5 from the point (1,2) is-
use the equation of S to find the value of theta.
Tangents are drawn from a point on the circle x2 + y2 = 25 to the ellipse 9x2 + 16y2 – 144= 0 then find the angle between the tangents.
tangents drawn from director circle to the ellipse make an angle of 90 degrees with themselves.
Tangents are drawn from a point on the circle x2 + y2 = 25 to the ellipse 9x2 + 16y2 – 144= 0 then find the angle between the tangents.
tangents drawn from director circle to the ellipse make an angle of 90 degrees with themselves.
The equation of the normal to the ellipse 
+ 
= 1, at the point (a cosθ, b sinθ) is-
differentiating a curve gives s the slope of tangent from where the slope of normal can be found out.
The equation of the normal to the ellipse + = 1, at the point (a cosθ, b sinθ) is-
differentiating a curve gives s the slope of tangent from where the slope of normal can be found out.
The equation of the normal at the point (2, 3) on the ellipse 9x2 + 16y2 = 180 is-
differentiating a curve gives us the slope of the tangent at any point in the curve. from that, we can find the slope of normal which will help s find the equation of normal at any point on the curve.
The equation of the normal at the point (2, 3) on the ellipse 9x2 + 16y2 = 180 is-
differentiating a curve gives us the slope of the tangent at any point in the curve. from that, we can find the slope of normal which will help s find the equation of normal at any point on the curve.
The equation of tangent to the ellipse x2 + 3y2 = 3 which is 
r to line 4y = x – 5 is-
slope of parallel lines are equal and product of perpendicular lines is -1.
this can be used to find the required slope.
The equation of tangent to the ellipse x2 + 3y2 = 3 which is r to line 4y = x – 5 is-
slope of parallel lines are equal and product of perpendicular lines is -1.
this can be used to find the required slope.
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
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 ellipse + = 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 + = 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 line x cos 
+ y sin = p will be a tangent to the conic + = 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 + y sin = p will be a tangent to the conic + = 1, if-
the tangent touches the curve at a single point and hence, has a single real solution to the equation.
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).
equation of tangent of an ellipse is given by :
y= m+ √(a2m2+b2)
this is used to find the values of m.
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.
the standard form of equation of tangents is obtained by substituting the values of coordinates into the equation of the curve
If 
+ 
= 
touches the ellipse + = 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 + = touches the ellipse + = 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.
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-
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 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-
the parametric form of a point on the ellipse gives us the coordinates of any point on the ellipse for a given angle.
