The condition so that the line lx - my - n -0 may touch the parabola y 2-8 xA- m2-8 lnB- m 2-2 lnC- 8 m 2- lnD- 2 m 2-ln

The correct option is D 2m^2=lnLine: lx + my+ n= 0 Parabola: y^2 =8x nbsp; So we can write, ⇒ y^2=8· (n+my)l ⇒ ly^2+8my+8n=0 The straight line touches the pa ...

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Standard XII

Mathematics

Rectangular Hyperbola

The condition...

Question

The condition so that the line $l x + m y + n = 0$ may touch the parabola $y^{2} = 8 x$

m^{2} = 8 l n

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m^{2} = 2 l n

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8 m^{2} = l n

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2 m^{2} = l n

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Solution

The correct option is D $2 m^{2} = l n$
Line:
$l x + m y + n = 0$
Parabola:
$y^{2} = 8 x$
So we can write,
$\Rightarrow y^{2} = 8 \cdot \frac{- (n + m y)}{l} \Rightarrow l y^{2} + 8 m y + 8 n = 0$
The straight line touches the parabola if the roots are same and real,
$∴ D = 0 \Rightarrow (8 m)^{2} = 4 \cdot l \cdot 8 n$
$\Rightarrow 2 m^{2} = l n$

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Similar questions

Q. The condition sot that the line

l x + m y + n = 0

may touch the parabola

y^{2} = 8 x

, is

Q. If the line

l x + m y + n = 0

touches the parabola

y^{2} = 4 a x

, prove that

l n = a m^{2}

Q. The condition that the line

l x + m y + n = 0

may be a normal to the parabola

y^{2} = 4 a x

Q. The condition that the straight line

l x + m y + n = 0

touches the parabola

x^{2} = 4 a y

Q. If the line

l x + m y + n = 0

touches the parabola

y^{2} = 4 a x

, then

l n =

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The condition so that the line lx+my+n=0 may touch the parabola y2=8x

The correct option is D 2m2=lnLine: lx+my+n=0 Parabola: y2=8x So we can write, ⇒y2=8⋅−(n+my)l⇒ly2+8my+8n=0 The straight line touches the parabola if the roots are same and real, ∴D=0⇒(8m)2=4⋅l⋅8n ⇒2m2=ln

The condition so that the line $l x + m y + n = 0$ may touch the parabola $y^{2} = 8 x$