Question

Determine the x and y intercepts of the ellipse equation \\(4y^2+9x^2=36

Answer 1

SOLUTION

TO DETERMINE

The x and y intercepts of the ellipse equation

$\sf{4 {y}^{2} + 9 {x}^{2} = 36}$

EVALUATION

Here the given equation of the ellipse is

$\sf{4 {y}^{2} + 9 {x}^{2} = 36}$

Which can be rewritten as

$\sf{9 {x}^{2} + 4 {y}^{2} = 36} \: \: \: - - - (1)$

The x - intercept is obtained by putting y = 0

Thus we get from Equation 1 by putting y = 0

$\sf{9 {x}^{2} = 36}$

$\sf{ \implies \: {x}^{2} = 4}$

$\sf{ \implies \: x = \pm \: 2}$

Hence the required x - intercept

= ( 2,0) & ( - 2,0)

The y - intercept is obtained by putting x = 0

Thus we get from Equation 1 by putting x = 0

$\sf{ 4 {y}^{2} = 36}$

$\sf{ \implies \: {y}^{2} =9}$

$\sf{ \implies \: y = \pm \: 3}$

Hence the required y - intercept

= ( 0,3 ) & ( 0,-3)

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