Home
Class 12
MATHS
Let A and B be two distinct points on th...

Let A and B be two distinct points on the parabola `y^2=4x`. If the axis of the parabola touches a circle of radius r having AB as its diameter, then find the slope of the line joining A and B .

A

`-1//r`

B

`1//r`

C

`2//r`

D

`-2//r`

Text Solution

Verified by Experts

The correct Answer is:
C, D
3,4

We have points `A(t_(1)^(2),2t_(1))andB(t_(2)^(2),2t_(2))` on the parabola `y^(2)=4x`.
For circle on AB as diameter center is `C((t_(1)^(2)+t_(2)^(2))/(2),(t_(1)+t_(2)))`.
Since circle is touching the x-axis, we have `r=|t_(1)+t_(2)|`
Also slope of AB, m `=(2t_(1)-2t_(2))/(t_(1)^(2)-t_(2)^(2))=(2)/(t_(1)+t_(2))=pm(2)/(r)`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Single Correct Answer Type|46 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise JEE ADVENCED SINGLE CORRECT ANSWER TYPE|2 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

Let A, B be two distinct points on the parabola y^(2)=4x . If the axis of the parabola touches a circle of radius r having AB as diameter, the slope of the line AB is

Let A(3, 0) and B(4, 1) are two points on the parabola y=(x-3)^(2) , find a point on this parabola where its tangent is parallel to the chord AB.

A is a point on the parabola y^2=4a x . The normal at A cuts the parabola again at point Bdot If A B subtends a right angle at the vertex of the parabola, find the slope of A Bdot

Let A(x_(1),y_(1)) and B(x_(2),y_(2)) be two points on the parabola y^(2) = 4ax . If the circle with chord AB as a dimater touches the parabola, then |y_(1)-y_(2)| is equal to

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

Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixed points on the parabola. Let C be a moving point on the parabola between Aa n dB such that the area of the triangle A B C is maximum. Then the coordinates of C are

A line L passing through the focus of the parabola y^2=4(x-1) intersects the parabola at two distinct points. If m is the slope of the line L , then

A P is perpendicular to P B , where A is the vertex of the parabola y^2=4x and P is on the parabola. B is on the axis of the parabola. Then find the locus of the centroid of P A Bdot

Let A(4,-4) and B(9,6) be points on the parabola y^(2)=4x. Let C be chosen on the on the arc AOB of the parabola where O is the origin such that the area of DeltaACB is maximum. Then the area (in sq. units) of DeltaACB is :

Let y=x+1 is axis of parabola, y+x-4=0 is tangent of same parabola at its vertex and y=2x+3 is one of its tangents. Then find the focus of the parabola.