Let $L_{1}$ be a straight line passing through the origin and $L_{2}$ be the straight line x + y=1. If the intercepts made by the circles $x^{2} + y^{2} - x + 3 y = 0$ on $L_{1}$ and $L_{2}$ are equal then which of the following equations can represent $L_{1} ?$

Q. The normal at

(4, 4)

to the parabola

y^{2} = 4 x

is given by

L = 0

. If

S : \frac{x^{2}}{36} + \frac{y^{2}}{20} - 1 = 0

be an ellipse, then

Q. Let

L

be a line passing through the point of intersection of the lines

x + 2 y + 1 = 0

and

2 x + 3 y - 1 = 0

. The locus of the circumcentre of the triangle formed by

L

and coordinate axes is

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Let L be a normal to the parabola y2=4x. If L passes through the point (9,6), the L is given by

The correct option is B y+3x−33=0Slope of Tangent at (9,6) will be 2ydydx=4⇒dydx=2y=26=13=m∴ Slope of L=−1m=−3L=y−6=−3(x−9)⇒y+3x−33=0Hence, (B).

Let $L$ be a normal to the parabola $y^{2} = 4 x$ . If $L$ passes through the point $(9, 6)$ , the $L$ is given by

The correct option is B $y + 3 x - 33 = 0$
Slope of Tangent at $(9, 6)$ will be $2 y \frac{d y}{d x} = 4$
$\Rightarrow \frac{d y}{d x} = \frac{2}{y} = \frac{2}{6} = \frac{1}{3} = m$
$∴$ Slope of $L = - \frac{1}{m} = - 3$
$L = y - 6 = - 3 (x - 9) \Rightarrow y + 3 x - 33 = 0$
Hence, $(B)$ .