Question
The equation of the tangent to the parabola y2 = 4x at the point (1, 2) is-
- x – y + 1 = 0
- x + y – 1 = 0
- x + y + 1 = 0
- x – y – 1 = 0
Hint:
find the slope of the curve at the given point and find the equation of straight line
The correct answer is: x – y + 1 = 0
x – y + 1 = 0
Slope of tangent = dy/dx = 2/y
Slope at 1,2 = 1
Equation of tangent : y-2 = 1(x-1)
y = x+1
x – y + 1 = 0
.
Slope of tangent = dy/dx
Equation of line: y-y1 = m(x-x1)
Related Questions to study
If a tangent to the parabola 4y2 = x makes an angle of 60º with the x- axis, then its point of contact is-
point of contact = (a/m2, 2a/m)
slope = tan ( angle made with the x axis)
this gives us the value of m
y^2 = x/4 = 4(1/16)x
a = 1/16
If a tangent to the parabola 4y2 = x makes an angle of 60º with the x- axis, then its point of contact is-
point of contact = (a/m2, 2a/m)
slope = tan ( angle made with the x axis)
this gives us the value of m
y^2 = x/4 = 4(1/16)x
a = 1/16
At which point the line x = my + 
touches the parabola x2 =4ay
the point of contact is the point of intersection between the 2 curves, the parabola and the line. this can be obtained by solving the two equations.
At which point the line x = my + touches the parabola x2 =4ay
the point of contact is the point of intersection between the 2 curves, the parabola and the line. this can be obtained by solving the two equations.
For what value of k, the line 2y – x + k = 0 touches the parabola x2 + 4y = 0-
when a quadratic equation has 2 equal roots, the D value is 0 . D= b^2 - 4ac.=0
this gives us the possible value(s) of k
For what value of k, the line 2y – x + k = 0 touches the parabola x2 + 4y = 0-
when a quadratic equation has 2 equal roots, the D value is 0 . D= b^2 - 4ac.=0
this gives us the possible value(s) of k
An element, X has the following isotopic composition, 
the weighted average atomic mass of the naturally- occurring element 'X' is closest to :
An element, X has the following isotopic composition, the weighted average atomic mass of the naturally- occurring element 'X' is closest to :
The line 
x + my + n = 0 will touch the parabola y2 = 4ax, if
a quadratic equation has equal roots if the D value is zero. this is the condition of the line touching the curve.
The line x + my + n = 0 will touch the parabola y2 = 4ax, if
a quadratic equation has equal roots if the D value is zero. this is the condition of the line touching the curve.
The straight line 2x + y –1= 0 meets the parabola y2 = 4x in
when D> 0, two real and distinct roots
when D=0, real and equal roots
when D<0 imaginary roots.
The straight line 2x + y –1= 0 meets the parabola y2 = 4x in
when D> 0, two real and distinct roots
when D=0, real and equal roots
when D<0 imaginary roots.
The line y = mx + c may touch the parabola y2 = 4a (x + a), if-
the solution of the two curves gives us the quadratic equation. D=0 gives us the required answer.
The line y = mx + c may touch the parabola y2 = 4a (x + a), if-
the solution of the two curves gives us the quadratic equation. D=0 gives us the required answer.
The straight line x + y = k touches the parabola y = x – x2, if k =
since only one point of contact is present, D=0 gives the real root.
The straight line x + y = k touches the parabola y = x – x2, if k =
since only one point of contact is present, D=0 gives the real root.
If the line x + y –1 = 0 touches the parabola y2 = kx, then the value of k is-
we can also solve for the two lines and make the D=0 for the resultant quadratic equation.
If the line x + y –1 = 0 touches the parabola y2 = kx, then the value of k is-
we can also solve for the two lines and make the D=0 for the resultant quadratic equation.
If length of the two segments of focal chord to the parabola y2 = 8ax are 2 and 4, then the value of a is-
the harmonic mean of the lengths (PS,QS) where S is the focus is equal to the half of latus rectum
the parametric coordinates of the ends of focal chords are (at^2, 2at) and (a/t^2,-2a/t)
If length of the two segments of focal chord to the parabola y2 = 8ax are 2 and 4, then the value of a is-
the harmonic mean of the lengths (PS,QS) where S is the focus is equal to the half of latus rectum
the parametric coordinates of the ends of focal chords are (at^2, 2at) and (a/t^2,-2a/t)
If PSQ is the focal chord of the parabola y2 = 8x such that SP = 6. Then the length SQ is-
the harmonic mean of the lengths (PS,QS) where S is the focus is equal to the half of latus rectum.
If PSQ is the focal chord of the parabola y2 = 8x such that SP = 6. Then the length SQ is-
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Length of the chord intercepted by the parabola y = x2 + 3x on the line x + y = 5 is
the distance between any two points is given by
√(x2-x1)2+(y2-y1)2
this formula is applied to the points of intersection which were calculated by solving the two equations .
Length of the chord intercepted by the parabola y = x2 + 3x on the line x + y = 5 is
the distance between any two points is given by
√(x2-x1)2+(y2-y1)2
this formula is applied to the points of intersection which were calculated by solving the two equations .
The length of the intercept made by the parabola 2y2 + 6y = 8 – 5x on y-axis is
the distance between two points on the y axis is just the difference in the y coordinates of the points.
The length of the intercept made by the parabola 2y2 + 6y = 8 – 5x on y-axis is
the distance between two points on the y axis is just the difference in the y coordinates of the points.
The length of the intercept made by the parabola x2 –7x +4y +12= 0 on x-axis is
distance between two points on the x axis is just the difference between the x coordinates of the two points, since y =0.
The length of the intercept made by the parabola x2 –7x +4y +12= 0 on x-axis is
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