COMEDK · Maths · 13. Parabola
In the parabola \(y^2=4 a x\) the length of the latus rectum is 6 units and there is a chord passing through its vertex and the negative end of the latus rectum. Then the equation of the chord is
- A \(2 x+y=0\)
- B \(x-2 y=0\)
- C \(x+2 y=0\)
- D \(2 x-y=0\)
Answer & Solution
Correct Answer
(A) \(2 x+y=0\)
Step-by-step Solution
Detailed explanation
The equation of the parabola is \(y^2 = 4ax\). The length of the latus rectum is given as \(4a = 6\), which implies \(a = \dfrac{6}{4} = \dfrac{3}{2}\). The coordinates of the vertex are \((0, 0)\). The endpoints of the latus rectum are \((a, 2a)\) and \((a, -2a)\). The negative…
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