TS EAMCET · Maths · Circle
If the line \(4 x-3 y+p=0(p+3\gt0)\) touches the circle \(x^2+y^2-4 x+6 y+4=0\) at the point \((h, k)\), then \(h-2 k=\)
- A \(-\frac{8}{5}\)
- B 2
- C \(\frac{6}{5}\)
- D 3
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
Centre \(\equiv(2,-3)\), Radius \(=3\) \(\Rightarrow\left|\frac{(4 \times 2)-(3 \times -3)+p}{5}\right|=3 \Rightarrow p+17=15 \Rightarrow p=-2\) Line is \(4 x-3 y-2=0\) \(\Rightarrow \frac{h-2}{4}=\frac{h+3}{-3}=\frac{-(8+9+p)}{25}=\frac{-3}{5}\) \(\Rightarrow h=\frac{-2}{5}\)…
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
- \(\mathbb{C f} a^x=b^y=c^z=d^w\), the value \(\alpha, x\left(\frac{1}{y}+\frac{1}{z}+\frac{1}{w}\right)\) isTS EAMCET 2007 Medium
- If the origin of a coordinate system is shifted to \((-\sqrt{2}, \sqrt{2})\) and the coordinate system is rotated anti-clockwise through an angle \(45^{\circ}\), then the point \(P(1,-1)\) in the original system has new coordinatesTS EAMCET 2015 Easy
- The solution of the differential equation , isTS EAMCET 2019 Easy
- Let \(S\) be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered 1 to 6 ) and let \(E_k=\{(a, b) \in S: a b=k\}\) for \(k \geq 1\). If \(p_k+P\left(E_k\right)\) for \(k \geq 1\), then the correct among the following, isTS EAMCET 2008 Medium
- The pole of the straight line \(x+4 y=4\) with respect to the ellipse \(x^2+4 y^2=4\) isTS EAMCET 2002 Easy
- The distance of the origin from the plane \(\mathbf{r} \cdot(3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-12 \hat{\mathbf{k}})=7\) measured parallel to the line \(\mathbf{r}=(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})+t(6 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})\) isTS EAMCET 2019 Medium
More PYQs from TS EAMCET
- If \(A=\left[\begin{array}{ll}0 & 5 \\ 0 & 0\end{array}\right]\) and \(f(x)=x+x^2+\ldots+x^{2018}\), then \(f(A)+I=\)TS EAMCET 2019 Easy
- If \(x=\tan 15^{\circ}, y=\operatorname{cosec} 75^{\circ}\) and \(z=4 \sin 18^{\circ}\), then :TS EAMCET 2006 Easy
- Three logic gates are connected as shown in the figure. If the inputs are \(\mathrm{A}=1, \mathrm{~B}=0\) and \(\mathrm{C}=1\), then the values of \(y_1, y_2\) and \(y_3\) respectively are
TS EAMCET 2025 Medium - If relative permeability of iron is 5500 , then its susceptibility isTS EAMCET 2020 Easy
- If \(A\) and \(B\) are arbitrary constants, then the differential equation having \(y=A e^{-x}+B \cos x\) as its general solution isTS EAMCET 2024 Medium
- If thenTS EAMCET 2022 Easy