If the curve $\frac{x^{2}}{4} + y^{2} = 1$ and $\frac{x^{2}}{a^{2}} + y^{2} = 1$ for suitable values of $^{'} a^{'}$ cut on four concyclic points, the equation of the circle passing through these points is

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} + y^{2} = 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $x^{2} + y^{2} = 1$
Let the equation of the circle be
$S_{1} + λ S_{2} = 0$
$\Rightarrow (\frac{x^{2}}{4} + y^{2} - 1) + λ (\frac{x^{2}}{a^{2}} + y^{2} - 1) = 0$
$\Rightarrow x^{2} (\frac{a^{2} + 4 λ}{4 a^{2} (1 + λ)}) + y^{2} = 1$
For the above equation to be a circle ;
$(\frac{a^{2} + 4 λ}{4 a^{2} (1 + λ)}) = 1$
Therefore equation of required circle is
$x^{2} + y^{2} = 1$

Suggest Corrections

Similar questions

Q. If the curves

\frac{x^{2}}{4} + y^{2} = 1

and

\frac{x^{2}}{a^{2}} + y^{2} = 1,

for suitable values of

a

cut on four concyclic points, the equation of the circle passing through these four points is:

Q. The locus of the point of intersection of two perpendicular tangents to the circle

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

For hyperbola $\frac{x^{2}}{25} - \frac{y^{2}}{12} = 1$ , and circle $x^{2} + y^{2} = 100$ , Four concyclic points are

For hyperbola $\frac{x^{2}}{25} - \frac{y^{2}}{16} = 1$ , and circle $x^{2} + y^{2} = 100$ , the ray from one of concyclic points passes through a focus.

Q. Equation of the circle passing through the point

(1, 1)

and point of intersection of circles

x^{2} + y^{2} = 6

and

x^{2} + y^{2} - 6 x + 8 = 0

Join BYJU'S Learning Program

If the curve x24+y2=1 and x2a2+y2=1 for suitable values of ′a′ cut on four concyclic points, the equation of the circle passing through these points is

The correct option is B x2+y2=1Let the equation of the circle be S1+λS2=0 ⇒(x24+y2−1)+λ(x2a2+y2−1)=0 ⇒x2(a2+4λ4a2(1+λ))+y2=1 For the above equation to be a circle ; (a2+4λ4a2(1+λ))=1 Therefore equation of required circle is x2+y2=1

If the curve $\frac{x^{2}}{4} + y^{2} = 1$ and $\frac{x^{2}}{a^{2}} + y^{2} = 1$ for suitable values of $^{'} a^{'}$ cut on four concyclic points, the equation of the circle passing through these points is