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A point R divides the line segment joining the points $P (1, 3)$ and $Q (1, 1)$ in the ratio $1 : λ$ If R is an interior point of the parabola $y^{2} = 4 x,$ then $λ$ can take a value in the interval

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−1<λ<35

−35<λ<5

−2<λ<2

−35<λ<1

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detailed solution

Correct option is D

Coordinates of R are =λ+1λ+1,3λ+1λ+1=1,3λ+1λ+1⇒For all values of λ x-coordinate of R is 1 and y-coordinate of R varies between –2 and 2⇒ −2<3λ+1λ+1<2.⇒ −35<λ<1

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A point R divides the line segment joining the points P(1, 3) and Q(1, 1) in the ratio 1:λ If R is an interior point of the parabola y2 = 4x, then λ can take a value in the interval

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A point R divides the line segment joining the points $P (1, 3)$ and $Q (1, 1)$ in the ratio $1 : λ$ If R is an interior point of the parabola $y^{2} = 4 x,$ then $λ$ can take a value in the interval