Home
Class 12
MATHS
If PQ is the focal chord of parabola y=x...

If PQ is the focal chord of parabola `y=x^(2)-2x+3` such that `P-=(2,3)`, then find slope of tangent at Q.

Text Solution

Verified by Experts

We know that tangents at the end point of focal chord are perpendicular.
For given parabola, `(dy)/(dx)=2x-2`
`:." "((dy)/(dx))_((2","3))=2` =slope of tangents at point P
Thus, slope of tangent at point Q is `-(1)/(2)`.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.6|8 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.7|9 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.4|13 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

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

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

The focal chord of the parabola y^2=a x is 2x-y-8=0 . Then find the equation of the directrix.

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 angle between the normal to the parabola y^(2)=4ax at point P and the focal chord passing through P is 60^(@) , then find the slope of the tangent at point P.

Let PQ be a focal chord of the parabola y^(2)=4ax . The tangents to the parabola at P and Q meet at point lying on the line y=2x+a,alt0 . If chord PQ subtends an angle theta at the vertex of y^(2)=4ax , then tantheta=

If the line y=3x+c touches the parabola y^2=12 x at point P , then find the equation of the tangent at point Q where P Q is a focal chord.

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

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

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