If the ellipse $9 x^{2} + 16 y^{2} = 144$ intercepts the line $3 x + 4 y = 12$ , then what is the length of the chord so formed?

5

units

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6

units

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8

units

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10

units

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Solution

The correct option is A $5$ units

Given equation of ellipse is $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$
From above figure we can see that line intercepts and intercepts made by ellipse are same

$∴$ length of chord = $\sqrt{4^{2} + 3^{2}}$
= $5$ units

Hence the correct option is 'A'

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Similar questions

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3

3 x + 4 y = 24

3 x + 4 y = 12

3 x - 4 y + 12 = 0

3 x + 2 y - 6 = 0

9 x^{2} - 24 x y + 16 y^{2} - 12 x + 16 y - 12 = 0

9 x^{2} - 24 x y + 16 y^{2} - 12 x + 16 y - 12 = 0

(5 x - 10)^{2} + (5 y + 15)^{2} = \frac{(3 x - 4 y + 7)^{2}}{4},

k

3 k =

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