The point (4, -3) with respect to the ellipse | vedclass

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Question

(c) Using the condition the point $({x_1},\,{y_1})$ lies

$(i)$ On the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} - 1 = 0$ if

$\f

Vedclass · Accepted Answer

Is outside the curve

Vedclass · Answer

(c) Using the condition the point $({x_1},\,{y_1})$ lies

$(i)$ On the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} - 1 = 0$ if

$\frac{{x_1^2}}{{{a^2}}} + \frac{{y_1^2}}{{{b^2}}} - 1 = 0$

$(ii)$ Outside the ellipse if $\frac{{x_1^2}}{{{a^2}}} + \frac{{y_1^2}}{{{b^2}}} - 1 > 0$

$(iii)$ Inside the ellipse if $\frac{{x_1^2}}{{{a^2}}} + \frac{{y_1^2}}{{{b^2}}} - 1 < 0$

Given ellipse is $\frac{{{x^2}}}{{1/4}} + \frac{{{y^2}}}{{1/5}} = 1$

 $\frac{{16}}{{1/4}} + \frac{9}{{1/5}} - 1 = 64 + 45 - 1 > 0$

Point $(4, -3)$ lies outside the ellipse.

The point $(4, -3)$ with respect to the ellipse $4{x^2} + 5{y^2} = 1$

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