Question

An ellipse with major axis $4$ and minor axis $2$ touches both the coordinate axis, then Locus of its center is

• A. $x^2-y^2=5$
• B. $x^2+y^2=5$
• C. $\frac{x^4}{4}+y^2=5$
• D. None of these

Answer 1

The correct option is D None of these

Given that,

Length of major axis $=2$

Length of minor axis $=2$

then, the centre of ellipse is $(1,1)$

If it touches both the co-ordinates axes in First quadeont

so, we use

$\frac{(x-1{)}^2}{2^2}+\frac{(y-1{)}^2}{2^2}=1$

$\Rightarrow (x-1{)}^2+(y-1{)}^2=4$

$\Rightarrow x^2-2x+1+y^2-2y+1=4$

$\Rightarrow x^2+y{Z}^2-2x-2y-2=0$

$\Rightarrow x^2+y^2-2x-2y-2=0$

Hence, this the answer.