Home
Class 12
MATHS
If chord BC subtends right angle at the ...

If chord BC subtends right angle at the vertex A of the parabola `y^(2)=4x` with `AB=sqrt(5)` then find the area of triangle ABC.

A

A. 20 sq. units

B

B. 10 sq. units

C

C. 40 sq. units

D

D. None of these

Text Solution

Verified by Experts

The correct Answer is:
20 sq. units
Let point B have coordinates `(t^(2),2t)`.

`AB=sqrt(5)`
`:." "t^(4)+4t^(2)=5`
`rArr" "(t^(2)-1)(t^(2)+5)=0`
`rArr" "t=pm1`
`:." "B-=(1,2)` (considering point B in first quadrant )
Now, BC subtends right angle at vertex A.
`:." "t t'=-4`
`:." "t'=-4`
So, C has coordinates (16,-8).
`:." " AC=sqrt(256+64)=sqrt(320)`
Therefore, area of triangle ABC
`=(1)/(2)ABxxAC`
`=(1)/(2)sqrt(5)sqrt(320)`
`=(1)/(2)sqrt(1600)=20` sq. units
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.2|17 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.3|7 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLES 5.14|1 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

A right-angled triangle A B C is inscribed in parabola y^2=4x , where A is the vertex of the parabola and /_B A C=pi/2dot If A B=sqrt(5), then find the area of A B Cdot

One double ordinate makes a right angle at the vertex of a parabola y^2=8x .the length of the double ordinate will be

Statement 1: Normal chord drawn at the point (8, 8) of the parabola y^2=8x subtends a right angle at the vertex of the parabola. Statement 2: Every chord of the parabola y^2=4a x passing through the point (4a ,0) subtends a right angle at the vertex of the parabola. (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Find the length of normal chord which subtends an angle of 90^0 at the vertex of the parabola y^2=4xdot

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

An equilateral triangle is inscribed in the parabola y^2=4a x , such that one vertex of this triangle coincides with the vertex of the parabola. Then find the side length of this triangle.

If the area of the triangle whose one vertex is at the vertex of the parabola, y^(2) + 4 (x - a^(2)) = 0 and the other two vertices are the points of intersection of the parabola and Y-axis, is 250 sq units, then a value of 'a' is

A(0,sqrt(2))andB(2sqrt(2),0) are two vertices of a triangle ABC and AB=BC . If the equation of the side BC be x=2sqrt(2) , then the area of triangle ABC is (in sq . Units )-

An equilateral triangle inscribe a parabola y^2 = 4ax . such that oneof the vertex of the triangle lies on the vertex of the parabola-. Find the,length of,the each side. of the triangle:

If the angles of the triangle ABC are in A.P. and b:c= sqrt3:sqrt2 then find the value of angleA