MHT CET · Maths · Application of Derivatives
The equation of the tangent parallel to \(y-x+5=0\) drawn to \(\frac{x^{2}}{3}-\frac{y^{2}}{2}=1\) is
- A \(x-y-1=0\)
- B \(x-y+2=0\)
- C \(x+y-1=0\)
- D \(x+y+2=0\)
Answer & Solution
Correct Answer
(A) \(x-y-1=0\)
Step-by-step Solution
Detailed explanation
Given hyperbola is \(\frac{x^{2}}{3}-\frac{y^{2}}{2}=1\) ...(i)
Equation of tangent parallel to \(y-x+5=0\) is
\(y-x+\lambda =0 \)
\( \Rightarrow y =x-\lambda ...(ii)\)
If line (ii) is a tangent to hyperbola (i), then
\(-\lambda=\pm \sqrt{3 x-2} \)
\( \left(\text { from } c=\pm \sqrt{a^{2} m^{2}-b^{2}}\right) \)
\( \Rightarrow -\lambda=\pm 1 \)
\( \Rightarrow \lambda=-1,+1\)
Put the values of \(\lambda\) in Eq. (ii), we get \(x-y-1=0 \quad\) and \(\quad x-y+1=0\) are the required tangents.
Equation of tangent parallel to \(y-x+5=0\) is
\(y-x+\lambda =0 \)
\( \Rightarrow y =x-\lambda ...(ii)\)
If line (ii) is a tangent to hyperbola (i), then
\(-\lambda=\pm \sqrt{3 x-2} \)
\( \left(\text { from } c=\pm \sqrt{a^{2} m^{2}-b^{2}}\right) \)
\( \Rightarrow -\lambda=\pm 1 \)
\( \Rightarrow \lambda=-1,+1\)
Put the values of \(\lambda\) in Eq. (ii), we get \(x-y-1=0 \quad\) and \(\quad x-y+1=0\) are the required tangents.
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