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Byju's Answer

Standard XII

Mathematics

Four Common Forms of Parabola Equation

M is the foot...

Question

$M$ is the foot of the perpendicular from a point $P$ on the parabola $y^{2} = 8 (x - 3)$ to its directrix and $S$ is the focus of the parabola. If $△ S P M$ is an equilateral triangle, the length of each side of the triangle is

2

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8

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Solution

The correct option is C $8$
Since $S P M$ is an equilateral triangle
$∠ S P M = 60^{0} \Rightarrow ∠ S M Z = 30^{0}$
FRom $△ S Z M$
$\frac{S Z}{S M} = sin 30^{0} \Rightarrow S M = 2 S Z \Rightarrow S M = 2 \times 4 = 8$
Hence length of each side of the triangle is $8$ .

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M is the foot of the perpendicular from a point P on the parabola y2=8(x−3) to its directrix and S is the focus of the parabola. If △SPM is an equilateral triangle, the length of each side of the triangle is

The correct option is C 8Since SPM is an equilateral triangle ∠SPM=600⇒∠SMZ=300FRom △SZMSZSM=sin300⇒SM=2SZ⇒SM=2×4=8Hence length of each side of the triangle is 8.

$M$ is the foot of the perpendicular from a point $P$ on the parabola $y^{2} = 8 (x - 3)$ to its directrix and $S$ is the focus of the parabola. If $△ S P M$ is an equilateral triangle, the length of each side of the triangle is

The correct option is C $8$
Since $S P M$ is an equilateral triangle
$∠ S P M = 60^{0} \Rightarrow ∠ S M Z = 30^{0}$
FRom $△ S Z M$
$\frac{S Z}{S M} = sin 30^{0} \Rightarrow S M = 2 S Z \Rightarrow S M = 2 \times 4 = 8$
Hence length of each side of the triangle is $8$ .