The equation of a parabola is y 2-4 x- Let P 1-3 and Q 1-1 are two points in the xy plane- Then-A- P and Q are exterior pointsB- P is an interior point while Q is an exterior pointC- P and Q are interior pointsD- P is an exterior point while Q is an interior point

The correct option is D P is an exterior point while Q is an interior pointHere, S≡ y^2 4x=0 S(1,3)=3^2 4.1 gt;0 ⇒ (1,3) is an exterior point. For the point ...

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Standard XII

Mathematics

Position of a Point W.R.T Parabola

The equation ...

Question

The equation of a parabola is $y^{2} = 4 x$ . Let P (1,3) and Q (1,1) are two points in the xy plane. Then,

P and Q are exterior points

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P is an interior point while Q is an exterior point

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P and Q are interior points

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P is an exterior point while Q is an interior point

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Solution

The correct option is D P is an exterior point while Q is an interior point
Here, $S \equiv y^{2} - 4 x = 0$
$S (1, 3) = 3^{2} - 4.1 > 0$
$\Rightarrow (1, 3) i s a n e x t e r i o r p o i n t . F o r t h e p o i n t (1, 1), S (1, 1) = 1^{1} - 4.1 < 0$
$\Rightarrow Q (1, 1)$ is an interior point

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The equation of a parabola is y2=4x. Let P (1,3) and Q (1,1) are two points in the xy plane. Then,

The correct option is D P is an exterior point while Q is an interior pointHere, S≡y2−4x=0 S(1,3)=32−4.1>0 ⇒(1,3)is an exterior point. Forthepoint(1,1),S(1,1)=11−4.1<0 ⇒Q(1,1) is an interior point

The equation of a parabola is $y^{2} = 4 x$ . Let P (1,3) and Q (1,1) are two points in the xy plane. Then,

The correct option is D P is an exterior point while Q is an interior point
Here, $S \equiv y^{2} - 4 x = 0$
$S (1, 3) = 3^{2} - 4.1 > 0$
$\Rightarrow (1, 3) i s a n e x t e r i o r p o i n t . F o r t h e p o i n t (1, 1), S (1, 1) = 1^{1} - 4.1 < 0$
$\Rightarrow Q (1, 1)$ is an interior point