वृत का समीकरण ज्ञात कीजिए :
केंद्र `(-a,-b)` और त्रिज्या `sqrt(a^2 -b^2)` इकाई

Options

A. `x^(2)+y^(2)+2ax+2by+2b^(2)=0`
B. `x^(2)+y^(*2)-2ax-2by-2b^(2)=0`
C. `x^(2)+y^(2)-2ax-2by+2b^(2)=0`
D. `x^(2)+y^(2)-2ax-2by+2a^(2)=0`

Answer

A

Explanation

We know that, equation of circle having centre (h,k) and radius r is `(x-yh)^(2)+(y-k)^(2)=r^(2)`
Here, centre=(-a,-b) and radius
`=sqrt(a^(2)-b^(2))`
`therefore` Reqruied equation of circle is
`(x+a^(2))+(y+b)^(2)=(sqrt(a^(2)-b^(2)))^(2)`
`impliesx^(2)+a^(2)+2axy^(2)+y^(2)+b^(2)+2by`
`=a^(2)-b^(2)`
`impliesx^(2)+2ax+y^(2)+2by+2b^(2)=0`