AP EAMCET · Maths · Pair of Lines
The equation of pair of straight lines parallel to \(X\)-axis and touching the circle \(x^2+y^2-6 x-4 y-12=0\)
- A \(y^2-4 y-21=0\)
- B \(y^2+4 y-21=0\)
- C \(y^2-4 y+21=0\)
- D \(y^2+4 y+21=0\)
Answer & Solution
Correct Answer
(A) \(y^2-4 y-21=0\)
Step-by-step Solution
Detailed explanation
Given circle is \(x^2+y^2-6 x-4 y-12=0\) \[ \begin{aligned} \text { Centre } & =(3,2) \\ \text { Radius } & =\sqrt{(3)^2+(2)^2+12}=\sqrt{9+4+12}=\sqrt{25} \\ r & =5 \end{aligned} \] Since, tangents are paralle to \(X\)-axis \(\therefore\) Let \(y=k\) be the tangent to the given…
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 in a \(\triangle A B C, r_1=2, r_2=3\) and \(r_3=6\), then \(a\) equals toAP EAMCET 2014 Hard
- If the roots of the equation \(4 x^3-12 x^2+11 x+k=0\) are in arithmetic progression, then \(k\) is equal toAP EAMCET 2004 Easy
- A straight line \(L\) with negative slope passes through the point \((1,1)\) and cuts the positive coordinate axes at the points \(A\) and \(B\). If \(O\) is the origin, then the minimum value of \(O A+O B\) as \(L\) varies, isAP EAMCET 2018 Easy
- \(e^{\log \left(\cos h^{-1} 2\right)}\) is equal to :AP EAMCET 2006 Medium
- If the line joining the points \(A(\alpha)\) and \(B(\beta)\) on the ellipse \(\frac{x^2}{25}+\frac{y^2}{9}=1\) is a focal chord, then one possible value of \(\cot \frac{\alpha}{2} \cdot \cot \frac{\beta}{2}\) isAP EAMCET 2019 Medium
- If the coefficients of \(r^{\text {th }},(r+1)^{\text {th }}\) and \((r+2)^{\text {th }}\) terms in the expansion of \((1+x) n\) are in the ratio of \(4: 15: 42\), then \(n-r=\)AP EAMCET 2024 Easy
More PYQs from AP EAMCET
- \(\begin{aligned} & \frac{1}{x(x+1)(x+2) \ldots(x+n)}=\frac{A_0}{x}+\frac{A_1}{x+1} \\ & +\ldots \frac{A_n}{x+n}, 0 \leq i \leq r \Rightarrow A_r \text { is equal to }\end{aligned}\)AP EAMCET 2012 Hard
- The distance between the centres of similitude of the circles \(x^2+y^2+6 x-8 y+16=0\) and \(x^2+y^2-2 x-2 y+\) \(1=0\) isAP EAMCET 2023 Hard
- If two subsets \(\mathrm{A}\) and \(\mathrm{B}\) are selected at random from a set \(\mathrm{S}\) containing \(\mathrm{n}\) elements, then the probability that \(\mathrm{A} \cap \mathrm{B}\) \(=\phi\) and \(\mathrm{A} \cup \mathrm{B}=\mathrm{S}\), isAP EAMCET 2023 Medium
- If \((\alpha, \beta)\) is the external centre of similitude of the circles \(x^2+y^2=3\) and \(x^2+y^2-2 x+4 y+4=0\), then \(\frac{\beta}{\alpha}=\)AP EAMCET 2025 Medium
- Consider the following.
Statement-I : The order of electronegativity of \(\mathrm{B}, \mathrm{Al}, \mathrm{In}, \mathrm{Tl}\) is
\(\mathrm{B}>\mathrm{T} l>\mathrm{A} l>\mathrm{In}\)
Statement-II : Boric acid is a weak protonic acid
The correct answer isAP EAMCET 2025 Medium - If \(f(x)=\frac{5 x \cdot \operatorname{cosec}(\sqrt{x})-1}{(x-2) \operatorname{cosec}(\sqrt{x})}\), then \(\lim _{x \rightarrow \infty} f\left(x^2\right)=\)AP EAMCET 2024 Easy