Equation of latus rectum of hyberbola 10 x -52-10 y -22-93 x -4 y -72 isA- y-1-5-3-4x-1-2B- y-1-5-3-4x-1-2C- y-1-5-3-4x-1-2D- y-1-5-3-4x-1-2

The correct option is B (x 1/2)^2 + (y 1/5)^2 = 9/4(3x + 4y 7/5)^2 ∴ focus at (1/2, 1/5) , directrix is 3x + 4y 7/5 = 0 ∴ Equation of latus rec ...

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Byju's Answer

Standard XII

Mathematics

Four Common Forms of Parabola Equation

Equation of l...

Question

Equation of latus rectum of hyberbola $(10 x - 5)^{2} + (10 y - 2)^{2} = 9 (3 x + 4 y - 7)^{2}$ is

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Solution

The correct option is A

${(x - \frac{1}{2})}^{2} + {(y - \frac{1}{5})}^{2} = \frac{9}{4} {(\frac{3 x + 4 y - 7}{5})}^{2}$
$∴$ focus at $(\frac{1}{2}, \frac{1}{5})$ , directrix is $\frac{3 x + 4 y - 7}{5}$ = 0

$∴$ Equation of latus rectum is $y - \frac{1}{5} = - \frac{3}{4} (x - \frac{1}{2})$

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Equation of latus rectum of hyberbola (10x−5)2+(10y−2)2=9(3x+4y−7)2 is

The correct option is A (x−12)2+(y−15)2=94(3x+4y−75)2 ∴ focus at (12,15) , directrix is 3x+4y−75 = 0 ∴ Equation of latus rectum is y–15=–34(x−12)

Equation of latus rectum of hyberbola $(10 x - 5)^{2} + (10 y - 2)^{2} = 9 (3 x + 4 y - 7)^{2}$ is

The correct option is A

${(x - \frac{1}{2})}^{2} + {(y - \frac{1}{5})}^{2} = \frac{9}{4} {(\frac{3 x + 4 y - 7}{5})}^{2}$
$∴$ focus at $(\frac{1}{2}, \frac{1}{5})$ , directrix is $\frac{3 x + 4 y - 7}{5}$ = 0

$∴$ Equation of latus rectum is $y - \frac{1}{5} = - \frac{3}{4} (x - \frac{1}{2})$