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  • Solve it, An ellipse is drawn by taking a diameter of the circle (x - 1)2 + y2 = 1 as its semiminor axis and a diameter of the circle x2 + (y - 2)2 = 4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coo

An ellipse is drawn by taking a diameter of the circle (x - 1)2 + y2 = 1 as its semiminor axis and a diameter of the circle               x2 + (y - 2)2 = 4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is

  • Option 1)

    4x2 + y2 = 4

  • Option 2)

    x2 + 4y2 = 8

  • Option 3)

    4x2 + y2 = 8

  • Option 4)

    x2 + 4y2 = 16

 

Answers (2)

best_answer

As leant in

Standard equation -

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

- wherein

a\rightarrow Semi major axis

b\rightarrow Semi minor axis

 

 

Equation of a circle -

\left ( x-h \right )^{2}+\left ( y-k \right )^{2}= r^{2}

- wherein

Circle with centre \left ( h,k \right ) and radius r.

 

 

(x-1)^{2}+y^{2}=1,r=1,\Rightarrow a=2

and\; \; x^{2}+(y-2)^{2}=4,r=2\Rightarrow b=4

\Rightarrow \; \; \frac{x^{2}}{16}+\frac{y^{2}}{4}=1\Rightarrow x^{2}+4y^{2}=16

 

 


Option 1)

4x2 + y2 = 4

This option is incorrect.

Option 2)

x2 + 4y2 = 8

This option is incorrect.

Option 3)

4x2 + y2 = 8

This option is incorrect.

Option 4)

x2 + 4y2 = 16

This option is correct.

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