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JEE Main 20246 AprilEvening Shift

Exam: JEE Main
Year: 2024
Date: 6 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Straight Lines

JEE Main 2024 · 6 April · Evening Shift · Mathematics · Straight Lines

If P(6,1) be the orthocentre of the triangle whose vertices are...

If

\mathrm{P}(6,1)

be the orthocentre of the triangle whose vertices are

\mathrm{A}(5,-2), \mathrm{B}(8,3)

and

\mathrm{C}(\mathrm{h}, \mathrm{k})

, then the point

C

lies on the circle: If P(6,1) be the orthocentre of the triangle whose vertices are A(5,-2), B(8,3) and C(h, k) , then the point C lies on

If P(6,1) be the orthocentre of the triangle whose vertices are A(5,-2), B(8,3) and C(h, k) , then the point C lies on

Options

A $x^2+y^2-61=0$
B $x^2+y^2-52=0$
C $x^2+y^2-65=0$
D $x^2+y^2-74=0$

Correct answer

C. $x^2+y^2-65=0$

Step-by-step solution

If P(6,1) be the orthocentre of the triangle whose vertices are A(5,-2), B(8,3) and C(h, k) , then the point C lies on

Slope of

A D=3

Slope of

\mathrm{BC}=-\frac{1}{3}

equation of

\mathrm{BC}=3 \mathrm{y}+\mathrm{x}-17=0

slope of

\mathrm{BE}=1

Slope of

\mathrm{AC}=-1

equation of

\mathrm{AC}

is

\mathrm{x}+\mathrm{y}-3=0

point

C

is

(-4,7)

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