TS EAMCET · Maths · Parabola
If \(\mathrm{L}(p, q), q>3\) is one end of the latus rectum of the parabola \((y-2)^2=3(x-1)\) then the equation of the tangent at L to this parabola is
- A \(2 x+y-7=0\)
- B \(4 x-4 y+7=0\)
- C \(2 x-y-3=0\)
- D \(2 x-3 y+7=0\)
Answer & Solution
Correct Answer
(B) \(4 x-4 y+7=0\)
Step-by-step Solution
Detailed explanation
The parabola is \((y-2)^2=3(x-1)\). This is in the form \((Y)^2 = 4a(X)\), where \(Y=y-2\), \(X=x-1\), and \(4a=3 \Rightarrow a=\frac{3}{4}\). The ends of the latus rectum are \((X=a, Y=\pm 2a)\). \(x-1 = \frac{3}{4} \Rightarrow x=\frac{7}{4}\).…
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