Question

The angles of elevation of a tower of height h situated at one end of the major axis of the ellipse $x^2+3y^2=3$ at two of its points B and C are ${45}^{\circ }$ each. Points A, B and C are situated on same side of minor axis. If BC subtends right angle at centre of the ellipse, then $h^2=$

• A. $\frac{5}{2}$
• B. $\frac{3}{2}$
• C. $\frac{9}{5}$
• D. $\frac{4}{3}$

Answer 1

The correct option is B $\frac{3}{2}$

Let $B(\sqrt{3}cos\theta ,sin\theta ),C(\sqrt{3}cos\theta ,-sin\theta )$


$m_{(}OB)\times m_{OC}=\frac{sin\theta }{\sqrt{3}cos\theta }\times \frac{-sin\theta }{\sqrt{3}cos\theta }=-1\Rightarrow ta{n}^2\theta =3\Rightarrow \theta =\frac{\pi }{3}{h}^2=A{D}^2=A{B}^2=(\sqrt{3}cos\theta -\sqrt{3}{)}^2+(sin\theta -0{)}^2={\left(\frac{\sqrt{3}}{2}\right)}^2+{\left(\frac{\sqrt{3}}{2}\right)}^2=\frac{3}{2}$