1. Tardigrade
  2. Question
  3. Mathematics
  4. Point A is the vertex of the parabola whose equation is y = x 2-2. Points B and C are the intersections of the parabola with the circle whose equation is x2+y2=8. The number of square units in the area of triangle ABC, is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Point $A$ is the vertex of the parabola whose equation is $y = x ^2-2$. Points $B$ and $C$ are the intersections of the parabola with the circle whose equation is $x^2+y^2=8$. The number of square units in the area of $\triangle ABC$, is

Conic Sections

Solution:

$ y = x ^2-2 ; x ^2+ y ^2=8 $
$x ^2= y +2 ; y ^2+ y +2=8 $
$y ^2+ y -6=0 \Rightarrow y ^2+3 y -2 y -6=0 $
$\Rightarrow( y +3)( y -2)=0 \Rightarrow y =2 \text { or } y =-3 \text { (rejected) } $
$\text { If } y =2 ; x =2 \text { or }-2$
$\therefore B (2,2) ; C =(-2,2) \text { and } A (0,-2)$
$\Rightarrow \text { Area of } \triangle ABC =\frac{4 \times 4}{2}=8$