If the curves (x2/4)+y2=1 and (x2/a2)+y2=1 cut on four concylic points for some suitable value of ' a ' then equation of circle passing through these four points, is

Question

If the curves (x2/4)+y2=1 and (x2/a2)+y2=1 cut on four concylic points for some suitable value of ' a ' then equation of circle passing through these four points, is (A) x2+y2=1 (B) x2+y2=2 (C) x2+y2=4 (D) None of these

Tardigrade Admin · Accepted Answer

Let equation of circle be ((x2/4)+y2-1)+λ((x2/a2)+y2-1)=0 ⇒ x2((1/4)+(λ/a2))+y2(1+λ)=(1+λ) ⇒ x2((a2+4 λ/4 a2(1+λ)))+y2=1

Q. If the curves $\frac{x ^{2}}{4} + y^{2} = 1$ and $\frac{x ^{2}}{a ^{2}} + y^{2} = 1$ cut on four concylic points for some suitable value of ' $a$ ' then equation of circle passing through these four points, is

$x^{2} + y^{2} = 1$

$x^{2} + y^{2} = 2$

$x^{2} + y^{2} = 4$

None of these

Let equation of circle be $(\frac{x ^{2}}{4} + y^{2} - 1) + λ (\frac{x ^{2}}{a ^{2}} + y^{2} - 1) = 0$
$\Rightarrow x^{2} (\frac{1}{4} + \frac{λ}{a ^{2}}) + y^{2} (1 + λ) = (1 + λ)$
$\Rightarrow x^{2} (\frac{a ^{2} + 4 λ}{4 a ^{2} ( 1 + λ )}) + y^{2} = 1$

Q. If the curves 4x2​+y2=1 and a2x2​+y2=1 cut on four concylic points for some suitable value of ' a ' then equation of circle passing through these four points, is

x2+y2=1

x2+y2=2

x2+y2=4