Question: The pole of the straight line $x + 4y = 4$ with respect to ellipse $x^{2} + 4y^{2} = 4$is...

Question

The pole of the straight line $x + 4y = 4$ with respect to ellipse $x^{2} + 4y^{2} = 4$ is

Answer 1

Solution

Equation of polar of $(x_{1},y_{1})$ w.r.t the ellipse is $\mathbf{x}\mathbf{x}_{\mathbf{1}}\mathbf{+ 4y}\mathbf{y}_{\mathbf{1}}\mathbf{= 4}$ .....(i)

Comparing with $x + 4y = 4$ .....(ii)

$\frac{x_{1}}{1} = \frac{4y_{1}}{4} = 1 \Rightarrow$ $x_{1} = 1,y_{1} = 1$ .

∴ Coordinates of pole $(x_{1},y_{1})$ = (1, 1)

Question: The pole of the straight line \(x + 4y = 4\) with respect to ellipse \(x^{2} + 4y^{2} = 4\)is...

Solution