Home
Class 12
MATHS
If PQ and Rs are normal chords of the pa...

If PQ and Rs are normal chords of the parabola `y^(2) = 8x` and the points P,Q,R,S are concyclic, then

A

tangents at P and R meet on X-axis

B

tangents at P and R meet on Y-axis

C

PR is parallel to Y-axis

D

PR is parallel to X-axis

Text Solution

Verified by Experts

The correct Answer is:
A, C
Equation of normal chords at `P(2t_(1)^(2),4t_(1))` and `R(2t_(2)^(2),4t_(2))` are `y + t_(1)x -4t_(1) -2t_(1)^(3) =0`
and `y + t_(2) x - 4t_(2) - 2t_(2)^(3) =0`.
Equation of curve through, P,Q,R,S is
`(y + t_(1)x -4t_(1)-2t_(1)^(3)) (y + t_(2)x -4t_(2) -2t_(2)^(3)) + lambda (y^(2) - 8x) =0`
P,Q,R,S are concyclic, `t_(1) + t_(2) =0` and `t_(1)t_(2) =1 + lambda`. Thus, point of intersection of tangents i.e., `(at_(1)t_(2),a (t_(1)+t_(2))` lies on X-axis. Slope of `PR = (2)/(t_(1)+t_(2))`
Hence, PR is parallel to Y-axis.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Matching Column Type|1 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Single Correct Answer Type|46 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

Length of the shortest normal chord of the parabola y^2=4ax is

The length of the common chord of the parabolas y^(2)=x and x^(2)=y is

Prove that the chord y-xsqrt(2)+4asqrt(2)=0 is a normal chord of the parabola y^2=4a x . Also find the point on the parabola when the given chord is normal to the parabola.

The normal to the parabola y^(2)=8x at the point (2, 4) meets the parabola again at the point-

PQ is any focal chord of the parabola y^(2)=8 x. Then the length of PQ can never be less than _________ .

If the normal chord of the parabola y^(2)=4x makes an angle 45^(@) with the axis of the parabola, then its length, is

If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , then the length of S Q is

The line 2x+y+lamda=0 is a normal to the parabola y^(2)=8x, is lamda =

If (2,-8) is at an end of a focal chord of the parabola y^2=32 x , then find the other end of the chord.

If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is