The equation of auxiliary circle of the ellipse 16 x 2-25 y 2-32 x -100 y -284 is A- x2-y2-2 x-4 y-20-0B- x2-y2-2 x-4 y-0C- x -12- y -22-400D- x-12-y-22-225

16x^2+25y^2+32x 100y=284 Rewrite the equation as (x+1)^225+(y 2)^216=1 So, the equation of auxiliary circle nbsp; (x+1)^2+(y 2)^2=25 ⇒ nbsp;x^2+y^2+2x 4y 20 ...

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Standard XII

Mathematics

Eccentric Angle : Ellipse

The equation ...

Question

The equation of auxiliary circle of the ellipse $16 x^{2} + 25 y^{2} + 32 x - 100 y = 284$ is

x^{2} + y^{2} + 2 x - 4 y - 20 = 0

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x^{2} + y^{2} + 2 x - 4 y = 0

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(x + 1)^{2} + (y - 2)^{2} = 400

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(x + 1)^{2} + (y - 2)^{2} = 225

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Solution

The correct option is A $x^{2} + y^{2} + 2 x - 4 y - 20 = 0$
$16 x^{2} + 25 y^{2} + 32 x - 100 y = 284$ Rewrite the equation as
$\frac{(x + 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1$
So, the equation of auxiliary circle
$(x + 1)^{2} + (y - 2)^{2} = 25 \Rightarrow x^{2} + y^{2} + 2 x - 4 y - 20 = 0$

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Similar questions

Q. The equation of auxiliary circle of hyperbola

25 y^{2} + 250 y - 16 x^{2} - 32 x + 209 = 0

Q. Then equation of auxiliary circle of the ellipse

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

Q. The equation of the circle having centre (1, –2) and passing through the point of intersection of the lines 3x + y = 14 and 3x + 5y = 18 is
(a) x² + y² – 2x + 4y – 20 = 0
(b) x² + y² – 2x – 4y – 20 = 0
(c) x² + y² + 2x – 4y – 20 = 0
(d) x² + y² + 2x + 4y – 20 = 0

The equation of a circle which cuts the three circles

$x^{2} + y^{2} - 3 x - 6 y + 14 = 0,$

$x^{2} + y^{2} - x - 4 y + 8 = 0$

$x^{2} + y^{2} + 2 x - 6 y + 9 = 0$

orthogonally is $- ------------- -$

Q. If

x = 3 sec θ - 2

and

y = 3 tan θ + 2

, then which of the following equation in

x, y

is correct?

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The equation of auxiliary circle of the ellipse 16x2+25y2+32x−100y=284 is

The correct option is A x2+y2+2x−4y−20=016x2+25y2+32x−100y=284 Rewrite the equation as (x+1)225+(y−2)216=1 So, the equation of auxiliary circle (x+1)2+(y−2)2=25⇒x2+y2+2x−4y−20=0

The equation of auxiliary circle of the ellipse $16 x^{2} + 25 y^{2} + 32 x - 100 y = 284$ is

The correct option is A $x^{2} + y^{2} + 2 x - 4 y - 20 = 0$
$16 x^{2} + 25 y^{2} + 32 x - 100 y = 284$ Rewrite the equation as
$\frac{(x + 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1$
So, the equation of auxiliary circle
$(x + 1)^{2} + (y - 2)^{2} = 25 \Rightarrow x^{2} + y^{2} + 2 x - 4 y - 20 = 0$