If the axes are rotated in anticlockwise through an angle of 90- then the equation x 2-4 ay will chane intoA- Y 2-4 aXB- X 2-4 aYC- X2-4 a YD- Y2-4 a X

The correct option is A Y^2=4aXRotating the coordinate axes by 90^∘ anticlockwise will transform the coordinates as x=Xcos(90^∘) Ysin(90^∘) and nbsp; y=Xsin ...

If the axes a...

Question

If the axes are rotated in anticlockwise through an angle of $90^{\circ}$ then the equation $x^{2} = 4 a y$ will chane into

Y^{2} = 4 a X

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X^{2} = - 4 a Y

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Y^{2} = - 4 a X

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

X^{2} = 4 a Y

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Solution

The correct option is A $Y^{2} = 4 a X$
Rotating the coordinate axes by $90^{\circ}$ anticlockwise will transform the coordinates as

$x = X cos (90^{\circ}) - Y sin (90^{\circ})$ and
$y = X sin (90^{\circ}) + Y cos (90^{\circ})$
$\Rightarrow x = - Y, y = X$

Substituting these values in the given equation
$(- Y)^{2} = 4 a (X)$

$\Rightarrow Y^{2} = 4 a X$

$∴$ the general equation is $Y^{2} = 4 a X$

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If the axes are rotated in anticlockwise through an angle of 90∘ then the equation x2=4ay will chane into

The correct option is A Y2=4aXRotating the coordinate axes by 90∘ anticlockwise will transform the coordinates as x=Xcos(90∘)−Ysin(90∘) and y=Xsin(90∘)+Ycos(90∘) ⇒x=−Y, y=X Substituting these values in the given equation (−Y)2=4a(X) ⇒Y2=4aX ∴ the general equation is Y2=4aX

If the axes are rotated in anticlockwise through an angle of $90^{\circ}$ then the equation $x^{2} = 4 a y$ will chane into