If `y=m_1x+c` and `y=m_2x+c` are two tangents to the parabola `y^2+4a(x+a)=0` , then `m_1+m_2=0` (b) `1+m_1+m_2=0` `m_1m_2-1=0` (d) `1+m_1m_2=0`

Question

If `y=m_1x+c` and `y=m_2x+c` are two tangents to the parabola `y^2+4a(x+a)=0` , then `m_1+m_2=0` (b) `1+m_1+m_2=0` `m_1m_2-1=0` (d) `1+m_1m_2=0`

If `y=m_1x+c` and `y=m_2x+c` are two tangents to the parabola `y^2+4a(x+a)=0` , then `m_1+m_2=0` (b) `1+m_1+m_2=0` `m_1m_2-1=0` (d) `1+m_1m_2=0`
A. `m_(1)+m_(2)=0`
B. `1+m_(1)+m_(2)=0`
C. `m_(1)m_(2)-1=0`
D. `1+m_(1)m_(2)=0`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - D
(4) Tangent `y=m_(1)x+candy=m_(2)x+c` intersect at (0,c) which lies on the directrix of the given parabola.
Hence, the tangents are perpendicular, for which `m_(1)m_(2)=-1`.

4 views Answered 2023-02-05 15:29