AP EAMCET · Maths · Circle
If the line \(4 x-3 y+7=0\) touches the circle \(x^2+y^2-6 x+4 y-12=0\) at \((\alpha, \beta)\), then \(\alpha+2 \beta=\)
- A \(3\)
- B \(-1\)
- C \(1\)
- D \(-3\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
Center of circle: \(C=(3, -2)\) Point of tangency \((\alpha, \beta)\) lies on line \(4x-3y+7=0\): \(4\alpha-3\beta=-7\) Radius from \(C\) to \((\alpha, \beta)\) is perpendicular to tangent line (slope \(4/3\)):…
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 \(f(x)=10 \cos x+(13+2 x) \sin x, \quad\) then \(f^{\prime \prime}(x)+f(x)\) is equal toAP EAMCET 2005 Hard
- If the locus of the mid points of the chords of the circle \(x^2+y^2=25\), which subtend a right angle at the origin is given by \(\frac{x^2}{a^2}+\frac{y^2}{a^2}=1\) then \(|a|=\)AP EAMCET 2024 Medium
- What is the formula for finding coefficient of variation, given \(\sigma=\) standard deviation and \(\bar{x}=\) mean \(\neq 0\) ?AP EAMCET 2020 Easy
- If \(\cosh x=\operatorname{cosec} \theta\), then \(\operatorname{coth} 2 \frac{x}{2}=\)AP EAMCET 2023 Hard
- If \(e_1\) and \(e_2\) are respectively the eccentricities of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and its conjugate hyperbola, then the line \(\frac{x}{2 e_1}+\frac{y}{2 e_2}=1\) touches the circle having centre at the origin, then its radius isAP EAMCET 2024 Medium
- \(\frac{1}{\cos 290^{\circ}}+\frac{1}{\sqrt{3} \sin 250^{\circ}}=\)AP EAMCET 2023 Easy
More PYQs from AP EAMCET
- \(\{n(n+1)(2 n+1): n \in Z\} \subset\)AP EAMCET 2005 Easy
- The equation of a normal to the circle \(x^2+y^2-2 x=0\) that is parallel to the line \(x+2 y-\) \(3=0\) isAP EAMCET 2020 Medium
- If \(A=35^{\circ}, B=15^{\circ}\) and \(C=40^{\circ}\), then \(\tan A \cdot \tan B+\tan B \cdot \tan C+\tan C \cdot \tan A\) is equal toAP EAMCET 2008 Medium
- What is the functional group present in serine, an aminoacid in addition to \(-\mathrm{NH}_2\) and \(-\mathrm{COOH}\) groups?AP EAMCET 2022 Easy
- A motor boat is moving in a river with velocity \(\overrightarrow{\mathrm{v}}=7 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-5 \hat{\mathrm{k}} \mathrm{ms}^{-1}\). If the flow of water offers resistive force \(\vec{F}=9 \hat{i}+3 \hat{j}-3 \hat{k} \quad N\), then the power of the boat isAP EAMCET 2023 Easy
- If slope of one line of \(a x^2+4 x y+y^2=0\) is 3 times the other, then the value of ' \(a\) ' isAP EAMCET 2020 Easy