Question

Equation of tangent to ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ in parametric form is

• A. $\frac{x\cos \theta }{a}+\frac{y\sin \theta }{b}=1$
• B. $\frac{x^2\cos \theta }{a^2}+\frac{y^2\sin \theta }{b^2}=1$
• C. None of the above
• D. $\frac{x\cos \theta }{a^2}+\frac{y\sin \theta }{b^2}=1$

Answer 1

The correct option is A $\frac{x\cos \theta }{a}+\frac{y\sin \theta }{b}=1$

As we know that the equation of tangent to an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is
$\frac{x{x}_1}{a^2}+\frac{y{y}_1}{b^2}=1$

For the equation of tangent in parametric form,
$\text{Put}{x}_1=a\cos \theta \text{and}{y}_1=b\sin \theta$
$\frac{x\cdot a\cos \theta }{a^2}+\frac{y\cdot b\sin \theta }{b^2}=1$
$\Rightarrow \frac{x\cos \theta }{a}+\frac{y\sin \theta }{b}=1$
This is the required equation of tangent to ellipse in parametric form.