Let the parabola $y=x^2+px-3$, meet the coordinate axes at the points P, Q and R. If the circle C with centre at $(-1,-1)$ passes through the points P, Q and R, then the area of $ riangle PQR$ is :

Question

Let the parabola $y=x^2+px-3$, meet the coordinate axes at the points P, Q and R. If the circle C with centre at $(-1,-1)$ passes through the points P, Q and R, then the area of $	riangle PQR$ is :

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] The circle through $R(0,-3)$ with centre $(-1,-1)$ has $r^2=5$: $x^2+y^2+2x+2y-3=0$. It meets the x-axis at $x=1,-3$, the roots of $x^2+px-3$ (so $p=2$). Area $=\frac12\cdot4\cdot3=6$. Answer (3).

Q. Let the parabola $y=x^2+px-3$, meet the coordinate axes at the points P, Q and R. If the circle C with centre at $(-1,-1)$ passes through the points P, Q and R, then the area of $\triangle PQR$ is :

Explanation

Reviewed by Dr. Abubacker

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