Test Index

Parabola Part 2

Section: Mathematics

© examsnet.com

Question : 22 of 51

Marks: +1, -0

Let the parabola

y=x^2+p x-3

, meet the coordinate axes at the points

P, Q

R

. If the circle

C

(-1,-1)

passes through the points

P, Q

R

, then the area of

\triangle PQR

[22 Jan 2025 Shift 1]

5
4
7
6

Solution: 👈: Video Solution

y=x^2+p x-3

is a parabola

at

x=0 \Rightarrow y=-3

Parabola cuts the

y

-axis at

(0,-3)

Equation of circle will be

\;(x+1)^2+(y+1)^2=(0+1)^2+(-3+1)^2

\; \Rightarrow (x+1)^2+(y+1)^2=5

\; \Rightarrow x^2+y^2+2x+2y-3=0

Now this circle cuts

x

-axis at

y=0

\;x^2+2x-3=0

\; \Rightarrow (x+3)(x-1)=0

\; \Rightarrow x=-3,1

\;(-3,0)\;\text{ and }\;(1,0)

Points

P, Q

and

R

are

(0,-3)(-3,0)

and

(1,0)

\;\;\text{Area of }\;(\triangle PQR)=\;\frac{1}{2}\begin{vmatrix}0 & -3 & 1\\-3 & 0 & 1\\1 & 0 & 1\end{vmatrix}

\;=\;\frac{1}{2}\times 12=6

© examsnet.com

Go to Question:

Prev Question

Next Question