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:

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!

None of these

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

Open in App

Solution

The correct option is B $x^{2} + y^{2} = 1$
Equation of the conic through point of intersection of given two ellipse is
$(\frac{x^{2}}{4} + y^{2} - 1) + λ (\frac{x^{2}}{a^{2}} + y^{2} - 1) = 0$
$\Rightarrow x^{2} (\frac{1}{4} + \frac{λ}{a^{2}}) + y^{2} (1 + λ) = 1 + λ$
$\Rightarrow x^{2} (\frac{a^{2} + 4 λ}{4 a^{2} (1 + λ)}) + y^{2} = 1$
This equation is a circle if $\frac{a^{2} + 4 λ}{4 a^{2} (1 + λ)} = 1$
$\Rightarrow$ Circle is $x^{2} + y^{2} = 1$

Suggest Corrections

Similar questions

Q. 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

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

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

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. The equation of the circle concentric with x² + y² − 3x + 4y − c = 0 and passing through (−1, −2) is
(a) x² + y² − 3x + 4y − 1 = 0
(b) x² + y² − 3x + 4y = 0
(c) x² + y² − 3x + 4y + 2 = 0
(d) none of these

Join BYJU'S Learning Program

If the curves 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 four points is:

The correct option is B x2+y2=1Equation of the conic through point of intersection of given two ellipse is(x24+y2−1)+λ(x2a2+y2−1)=0⇒x2(14+λa2)+y2(1+λ)=1+λ⇒x2(a2+4λ4a2(1+λ))+y2=1This equation is a circle if a2+4λ4a2(1+λ)=1⇒ Circle is x2+y2=1

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: