Question

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 the circle.

(1) \(x^{2}+y^{2}-65=0\)

(2) \(x^{2}+y^{2}-74=0\)

(3) \(x^{2}+y^{2}-61=0\)

(4) \(x^{2}+y^{2}-52=0\)

Answer 1

Correct option is (1) \(x^{2}+y^{2}-65=0\)

Slope of \(\mathrm{AD}=3\)

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 AC is \(\,\mathrm{x}+\mathrm{y}-3=0\)

\(point \,C\, is \,(-4,7)\)