JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the tangents drawn at the points \(P\) and \(Q\) on the parabola \(y^{2}=2 x-3\) intersect at the point \(R(0,1)\), then the orthocentre of the triangle \(PQR\) is.
- A \((0,1)\)
- B \((2,-1)\)
- C \((6,3)\)
- D \((2,1)\)
Answer & Solution
Correct Answer
(B) \((2,-1)\)
Step-by-step Solution
Detailed explanation
\(y^{2}=2 x-3\) Equation of chord of contact \(PQ : r =0\) \(y x 1=(x+0)-3\) \(y=x-3\) from \((1)\) and \((2)\) \(( x \cdot 3)^{2}=2 x -3\) \(x ^{2}-8 x +12=0\) \(( x -2)( x -6)=0\) \(x =2\) or \(6\) \(y =-1\) or \(3\) \(MPQ =\frac{1}{4}=1\) \(MQR =\frac{2}{6}=\frac{1}{3}\)…
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