Question

I. The straight line $x+y=a$ will be a tangent to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ if $a=\pm 5$
II. The straight line $x+y=a$ will be a tangent to the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ if $a=\pm 7$.
Which of the above statements is correct?

• A. only II
• B. only I
• C. both I and II
• D. Neither I nor II

Answer 1

Answer: (B)

only I

Using the following concept

A line is tangent to an ellipse if for a lime $y=mx+c$

$c^2=a^2{m}^2+b^2$

And the given line is tangent for a hyperbola if and only if $c^2=a^2{m}^2-b^2$

With this we can see that only statement I is true.