Family of curves which makes an angle -4 whith the family of hyperbola xy - c 2 is A- x2-4 x y-y2-kB- x2-2 x y-y2-kC- x2-2 x y-y2-kD- x2-x y-y2-k

The correct options are B x^2+2xy y^2=k C x^2 2xy y^2=k xy=c^2⇒dy/dx=m_1= y/x m_2=dy/dx ⇒ | dy/dx+y/x/1 ( dy/dx ) ( y/x ) |=1 ⇒ x^2+2xy y^2=k (or) x^2 ...

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Byju's Answer

Standard XII

Mathematics

Angle of Intersection of Two Curves

Family of cur...

Question

Family of curves which makes an angle $\frac{π}{4}$ whith the family of hyperbola $x y = c^{2}$ is

x^{2} - 4 x y - y^{2} = k

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x^{2} + 2 x y - y^{2} = k

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x^{2} - 2 x y - y^{2} = k

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

x^{2} + x y - y^{2} = k

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct options are
B $x^{2} + 2 x y - y^{2} = k$

C $x^{2} - 2 x y - y^{2} = k$

$x y = c^{2} \Rightarrow \frac{d y}{d x} = m_{1} = - \frac{y}{x} m_{2} = \frac{d y}{d x} \Rightarrow ∣ ∣ ∣ ∣ \frac{\frac{d y}{d x} + \frac{y}{x}}{1 - (\frac{d y}{d x}) (\frac{y}{x})} ∣ ∣ ∣ ∣ = 1 \Rightarrow x^{2} + 2 x y - y^{2} = k (o r) x^{2} - 2 x y - y^{2} = k$

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Family of curves which makes an angle π4 whith the family of hyperbola xy=c2 is

The correct options are B x2+2xy−y2=k C x2−2xy−y2=k xy=c2⇒dydx=m1=−yxm2=dydx⇒∣∣ ∣∣dydx+yx1−(dydx)(yx)∣∣ ∣∣=1⇒x2+2xy−y2=k (or) x2−2xy−y2=k

Family of curves which makes an angle $\frac{π}{4}$ whith the family of hyperbola $x y = c^{2}$ is