Question

The equation $\frac{7}{r}=5+3\cos \theta +4\sin \theta$ represents

• A. a parabola
• B. an ellipse
• C. a hyperbola
• D. a rectangular hyperbola

Answer 1

The correct option is A a parabola

We know that eccentricity of the parabola $\frac{l}{r}=a+b\cos \theta +c\sin \theta$ ... (i) is given by
$e=\frac{\sqrt{c^2+b^2}}{\mid a\mid }$ ... (ii)
Now comparing equation (i) with the given equation, we get
$a=5,b=3$ and $c=4$
Substituting these values in the equation (ii), we get
$e=\frac{\sqrt{3^2+4^2}}{\mid 5\mid }=1,$ which is true in case of parabola.
Hence, the correct answer is 'A'.