The straight line x + y = sqrt 2 p will touch | vedclass

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Question

(d) The condition for the line $y = mx + c$ will touch the hyperbola

$\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ is ${c^2} = {a^2}{m^2}

Vedclass · Accepted Answer

$2{p^2} = 5$

Vedclass · Answer

(d) The condition for the line $y = mx + c$ will touch the hyperbola

$\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ is ${c^2} = {a^2}{m^2}$$ - {b^2}$

Here $m = - 1$, $c = \sqrt 2 p,$  ${a^2} = 9,\,\,{b^2} = 4$

 We get $2{p^2} = 5.$

The straight line $x + y = \sqrt 2 p$ will touch the hyperbola $4{x^2} - 9{y^2} = 36$, if

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