JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let A be the focus of the parabola \(y^{2}=8x.\) Let the line \(y=mx+c\) intersect the parabola at two distinct points B and C. If the centroid of the triangle ABC is \((\frac{7}{3},\frac{4}{3})\) , then \((BC)^{2}\) is equal to:
- A 41
- B 80
- C 89
- D 32
Answer & Solution
Correct Answer
(B) 80
Step-by-step Solution
Detailed explanation
Coordinates of centroid of triangle ABC are \(\frac{2}{3}(t_{1}^{2}+t_{2}^{2}+1)=\frac{7}{3}\Rightarrow t_{1}^{2}+t_{2}^{2}=\frac{5}{2}\) \(\frac{4}{3}(t_{1}+t_{2})=\frac{4}{3}\Rightarrow t_{1}+t_{2}=1\)…
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