JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let O be the vertex of the parabola \( x^{2}=4y \) and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio 2 : 3 be the conic C. Then the equation of the chord of C, which is bisected at the point (1, 2), is:
- A 5x - y - 3 = 0
- B 4x - 5y + 6 = 0
- C x - 2y + 3 = 0
- D 5x - 4y + 3 = 0
Answer & Solution
Correct Answer
(D) 5x - 4y + 3 = 0
Step-by-step Solution
Detailed explanation
\( h = \frac{4t}{5}\) \(k = \frac{2(t^2)}{5}\) = \(\frac{2}{5}(\frac{5h}{4})^2\) \(8k = 5h^2\) \(\Rightarrow 5x^2=8y \) \( T=S_1 \) \(5\left( xx _1\right)-4\left( y + y _1\right)=5 x _1^2-8 y _1\) \(5(x)-4(y+2)=5-8.2\) \(5 x-4 y+3=0\)
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