AP EAMCET · Maths · Parabola
If the directrix of the parabola \(x^2+4 y-6 x+\lambda=0\) is \(y+1=0\), then which of the following is correct?
- A \(\lambda=-17\)
- B \(\lambda=-19\)
- C focus is \((3,-3)\)
- D vertex is \((3,-3)\)
Answer & Solution
Correct Answer
(C) focus is \((3,-3)\)
Step-by-step Solution
Detailed explanation
Parabola is \((x-3)^2=-4\left(y-\left(\frac{\lambda-9}{4}\right)\right)\) Equation of direction is \(y=\frac{\lambda-9}{4}+1\) \(\therefore\) As direction is \(y+1=0, \frac{\lambda-9}{4}+1=-1\) \(\lambda=1\) \(\therefore\) Vertex is \((3,-2)\) and focus is \((3,-3)\).
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