Question

The condition that the line $\frac{x}{p}+\frac{y}{p}=1$ o be tangent to $\frac{x^z}{a^z}+\frac{y^z}{b^z}=1$ is

• A. $\frac{a^z}{p^z}-\frac{b^z}{q^z}$ = 1
• B. $\frac{a^z}{p^z}-\frac{b^z}{q^z}$ = 1
• C. $\frac{a^z}{q^z}-\frac{b^z}{p^z}$ = 1
• D. $\frac{a^z}{q^z}-\frac{b^z}{p^z}$ = 1

Answer 1

The correct option is B

$\frac{a^z}{p^z}-\frac{b^z}{q^z}$ = 1

$\frac{x}{p}+\frac{y}{p}=1$ $\frac{x^z}{a^z}-\frac{y^z}{b^z}=1$

$\frac{y}{p}=\frac{-x}{p}+1$

y = $\frac{-q}{p}x+q$

$q^2=a^2\frac{q^z}{p^z}-b^2$

$\Rightarrow$ $a^2{q}^2-b^2{p}^2=p^2{q}^2$

$\Rightarrow$ $\frac{a^2}{p^2}-\frac{b^2}{q^2}$ = 1