Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaMiscellaneous/MixedMedium2 minPYQ_2007

MathematicsMediumsingle choice

Passage / Comprehension

Paragraph:Consider the circle $x^{2} + y^{2} = 9$ and the parabola $y^{2} = 8 x$ . They intersect at $P$ and $Q$ in the first and the fourth quadrants, respectively. Tangents to the circle at $P$ and $Q$ intersect the $X$ -axis at $R$ and tangents to the parabola at $P$ and $Q$ intersect the $X$ -axis at $S$

.Question:The ratio of the areas of the $△ PQS$ and $△ PQR$ is

Options:

Answer:

Solution:

Coordinates of $P$ and $Q$ are $(1, 22)$ and $(1, - 22)$ .
Area of $△ PQR = \frac{1}{2} \cdot 42 \cdot 8 = 162$ Area of $△ PQS = \frac{1}{2} \cdot 42 \cdot 2 = 42$ Ratio of area of $△ PQS$ and $△ PQR$ is $1 : 4$ .

Stream:JEE_ADVSubject:MathematicsTopic:ParabolaSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: PYQ_2007

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