TS EAMCET · Maths · Parabola
The normal at a point on the parabola \(\mathrm{y}^2=4 \mathrm{x}\) passes through \((5,0)\). If there are two more normals to this parabola passing through \((5,0)\), then the equation of one of these normals is
- A \(2 x-y-10=0\)
- B \(x+y-5=0\)
- C \(\sqrt{3} x+2 y+5 \sqrt{3}=0\)
- D \(\sqrt{3} x-y-5 \sqrt{3}=0\)
Answer & Solution
Correct Answer
(D) \(\sqrt{3} x-y-5 \sqrt{3}=0\)
Step-by-step Solution
Detailed explanation
(d) \(\because\) There are 3 normals through \((5,0)\). Equation of normal to parabola \(y^2=4 a x\) \[ y=m x-2 a m-a m^3 \] For \(y^2=4 x, a=1\) \[ \therefore y=m x-2 m-m^3 \] \(\because \quad\) It passes through \((5,0)\)…
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