Question

A tangent having slope of $-\frac{4}{3}$ to the ellipse $\frac{x^2}{18}+\frac{y^2}{32}=1$ intersects the major and minor axes in points $A$ and $B$ respectively. If $O$ is the origin, find the area of $△OAB$.

• A. $12$
• B. $24$
• C. $48$
• D. $60$

Answer 1

The correct option is B $24$

$Equationoftangentwithslopem=-\frac{4}{3}a=3\sqrt{2}b=4\sqrt{2}is:y=mx\pm \sqrt{{\left(am\right)}^2+b^2}Or,y+\frac{4x}{3}=\pm \sqrt{32+32}Or,3y+4x=\pm 24Consideringonlyinthefirstquadrant:X-InterceptX=6Y-interceptY=8Areaof△AOB=\frac{1}{2}\ast 6\ast 8=24$

Option [B]