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Parabola question

2022 · Shift 1 · Q31

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PYQ Library
JEE Advanced
Mathematics
Parabola
2022 · Shift 1 · Q31

Parabola question

2022 · Shift 1 · Q31

JEE AdvancedMathematicsParabolaMultiple correct+4 / −2

Consider the parabola

y^{2}=4 x

. Let

S

be the focus of the parabola. A pair of tangents drawn to the parabola from the point

P=(-2,1)

meet the parabola at

P_{1}

and

P_{2}

. Let

Q_{1}

and

Q_{2}

be points on the lines

S P_{1}

and

S P_{2}

respectively such that

P Q_{1}

is perpendicular to

S P_{1}

and

P Q_{2}

is perpendicular to

S P_{2}

. Then, which of the following is/are TRUE?

A
$S Q_{1}=2$
B
$Q_{1} Q_{2}=\frac{3 \sqrt{10}}{5}$
C
$P Q_{1}=3$
D
$S Q_{2}=1$

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