Equation of the auxiliary circle of the ellipse x2-12-y2-18-1

Name: JEE- Grade 11- Mathematics- Ellipse- Session 02- W05
Uploaded: 2022-07-04T10:36:42+05:30
Description: The correct option is B x^2+y^2=18Given equation of ellipse is nbsp; x^212+y^218=1 a^2=12, b^2=18, a lt;b Equation of auxiliary circle is x^2+y^2=b^2 ⇒ x^ ...

The correct option is B x^2+y^2=18Given equation of ellipse is nbsp; x^212+y^218=1 a^2=12, b^2=18, a lt;b Equation of auxiliary circle is x^2+y^2=b^2 ⇒ x^ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Eccentric Angle : Ellipse

Equation of t...

Question

Equation of the auxiliary circle of the ellipse
$\frac{x^{2}}{12} + \frac{y^{2}}{18} = 1$ is

x^{2} + y^{2} = 9

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

x^{2} + y^{2} = 18

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

x^{2} + y^{2} = 12

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

x^{2} + y^{2} = 30

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

Open in App

Solution

The correct option is B $x^{2} + y^{2} = 18$
Given equation of ellipse is
$\frac{x^{2}}{12} + \frac{y^{2}}{18} = 1$
$a^{2} = 12, b^{2} = 18, a < b$
Equation of auxiliary circle is
$x^{2} + y^{2} = b^{2}$
$\Rightarrow x^{2} + y^{2} = 18$

Suggest Corrections

Similar questions

Q. Assertion :Tangents drawn from any point on the circle

x^{2} + y^{2} = 225

to the ellipse

\frac{x^{2}}{144} + \frac{y^{2}}{81} = 1

are at right angle. Reason: Equation of the auxiliary circle of the ellipse

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

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

Q. Equation of the auxiliary circle of the ellipse

\frac{x^{2}}{12} + \frac{y^{2}}{18} = 1

Q. The equation of auxiliary circle of the ellipse

16 x^{2} + 25 y^{2} + 32 x - 100 y = 284

Q. The equation of the auxiliary circle of the hyperbola

\frac{x^{2}}{64} - \frac{y^{2}}{36} = 1

Equation of the locus of the pole with respect to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ of any tangent line to the auxiliary circle is the curve
$\frac{x^{2}}{a^{4}} + \frac{y^{2}}{b^{4}} = λ^{2}$ where

Join BYJU'S Learning Program

Explore more

Eccentric Angle : Ellipse

Standard XII Mathematics

Join BYJU'S Learning Program

Equation of the auxiliary circle of the ellipse x212+y218=1 is

The correct option is B x2+y2=18Given equation of ellipse is x212+y218=1 a2=12, b2=18,a<b Equation of auxiliary circle is x2+y2=b2 ⇒x2+y2=18

Equation of the auxiliary circle of the ellipse
$\frac{x^{2}}{12} + \frac{y^{2}}{18} = 1$ is

The correct option is B $x^{2} + y^{2} = 18$
Given equation of ellipse is
$\frac{x^{2}}{12} + \frac{y^{2}}{18} = 1$
$a^{2} = 12, b^{2} = 18, a < b$
Equation of auxiliary circle is
$x^{2} + y^{2} = b^{2}$
$\Rightarrow x^{2} + y^{2} = 18$