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 the slope of the line joining `A and B` can be (A) `- 1/r` (B) `1/r` (C) `2/r` (D) `- 2/r`

A

`-1//r`

B

`1//r`

C

`2//r`

D

`-2//r`

Text Solution

Verified by Experts

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

Similar Questions

Explore conceptually related problems

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 diameter touches the parabola, then |y_(1)-y_(2)|=

Let P and Q be the points on the parabola y^(2)=4x so that the line segment PQ subtends right angle If PQ intersects the axis of the parabola at R, then the distance of the vertex from R is

A circle of radius r drawn on a chord of the parabola y^(2)=4ax as diameter touches theaxis of the parabola.Prove that the slope of the chord is (2a)/(r)

The normal to the parabola y^(2)=4x at P(9, 6) meets the parabola again at Q. If the tangent at Q meets the directrix at R, then the slope of another tangent drawn from point R to this parabola is

If the sum of the areas of two circles with radii r_1 and r_2 is equal to the area of a circle of radius r , then r_1^2 +r_2^2 (a) > r^2 (b) =r^2 (c)

Locus of the mid-point of the line joining (3,2) and point on (x^2+y^2=1) is a circle of radius r . Find r

A line L passing through the focus of the parabola y^(2)=4(x-1) intersects the parabola at two distinct points.If m 1m in R( d) none of these

Let P be a point on the parabola y^(2) - 2y - 4x+5=0 , such that the tangent on the parabola at P intersects the directrix at point Q. Let R be the point that divides the line segment PQ externally in the ratio 1/2 : 1. Find the locus of R.