JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(A,B\) and \(C\) be the vertices of a variable right angled triangle inscribed in the parabola \(y^2=16x\). Let the vertex \(B\) containing the right angle be \((4,8)\) and the locus of the centroid of \(\triangle ABC\) be a conic \(C_o\). Then three times the length of latus rectum of \(C_o\) is ______
- A 13
- B 14
- C 15
- D 16
Answer & Solution
Correct Answer
(D) 16
Step-by-step Solution
Detailed explanation
The equation of the parabola is \(y^2 = 16x\), which gives \(a = 4\). Any point on the parabola can be taken as \((4t^2, 8t)\). The vertex \(B\) is given as \((4,8)\), which corresponds to the parameter \(t = 1\). Let the parameters for vertices \(A\) and \(C\) be \(t_1\) and…
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