AP EAMCET · Maths · Hyperbola
The equation of the common tangent drawn to the curves \(y^2=8 x\) and \(x y=-1\) is
- A \(y = 2x + 1\)
- B \(2y = x + 6\)
- C \(y = x + 2\)
- D \(3y = 8x + 2\)
Answer & Solution
Correct Answer
(C) \(y = x + 2\)
Step-by-step Solution
Detailed explanation
Let \(P\left(t, \frac{-1}{t}\right)\) be a point on \(x y=-1\) Equation of tangent of \(P\) \(\begin{aligned} & =\frac{1}{2}\left[x\left(\frac{-1}{t}\right)+x y\right]=-1-x+t^2 y=-2 t \\ & y=\frac{x}{t^2}+\frac{2}{t} \end{aligned}\) This is also at tangent of \(y^2=8 x\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(\left(1+x+x^2+x^3\right)^5=\sum_{k=0}^{15} a_k x^k\), then \(\sum_{k=0}^7 a_{2 k}\) is equal toAP EAMCET 2008 Medium
- If the system of equations \(a_1 x+b_1 y+c_1 z=0\), \(a_2 x+b_2 y+c_2 z=0, \quad a_3 x+b_3 y+c_3 z=0\) has only trivial solution, then the rank of \(\left[\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right]\) isAP EAMCET 2024 Easy
- Find the conjugate of \(\frac{5 i}{7+i}\)AP EAMCET 2020 Easy
- \(\int \frac{x^2-1}{x^3 \sqrt{2 x^4-2 x^2+1}} d x=\)AP EAMCET 2023 Medium
- If a square matrix \(A\) is such that \(\left(A^T-\frac{1}{2} I\right)\left(A-\frac{1}{2} I\right)\) \(=\left(A^T+\frac{1}{2} I\right)\left(A+\frac{1}{2} I\right)=I\), where \(I\) is a unit matrix, then \(A\) isAP EAMCET 2021 Easy
- In Argand plane, the quadrant in which \(\frac{1+2 i}{1-i}\) lies isAP EAMCET 2017 Easy
More PYQs from AP EAMCET
- If \(\vec{a}, \vec{b}\) are the two non collinear vectors. then \(|\vec{b}| \vec{a}+|\vec{a}| \vec{b}\) representsAP EAMCET 2024 Easy
- The maximum value of \(12 \sin x-5 \cos x+3\) isAP EAMCET 2024 Easy
- The locus of the complex number Z such that \(\arg \left(\frac{Z-1}{Z+1}\right)=\frac{\pi}{4}\) isAP EAMCET 2024 Easy
- If \(\mathrm{A}(2,-1,1), \mathrm{B}(2,5,1)\) and \(\mathrm{C}(0,-2,3)\) are the vertices of a triangle. If D is the point of intersection of the side BC and the internal angular bisector of angle A, then \(\mathrm{AD}=\)AP EAMCET 2025 Medium
- An inorganic compound \((A)\) made of two most occurring elements in the Earth's crust and used in building construction, when made to react with carbon, forms a poisonous gas \((B)\) which is most stable diatomic molecule, compound \((A)\) and \((B)\) areAP EAMCET 2021 Easy
- The solution of the differential equation \(x y^2 d y-\left(x^3+y^3\right) d x=0\) isAP EAMCET 2008 Medium