AP EAMCET · Maths · Circle
The number of common tangents to the circles \(x^2+y^2+2 x+8 y-23=0\) and \(x^2+y^2-4 x-10 y+19=0\), is
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
C1 \( = (-1, -4) \), R1 \( = \sqrt{(-1)^2 + (-4)^2 - (-23)} = \sqrt{40} = 2\sqrt{10} \) C2 \( = (2, 5) \), R2 \( = \sqrt{(2)^2 + (5)^2 - 19} = \sqrt{10} \) d \( = \sqrt{(2 - (-1))^2 + (5 - (-4))^2} = \sqrt{3^2 + 9^2} = \sqrt{9 + 81} = \sqrt{90} \) R1 + R2…
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
- Assertion (A)
\[
\int_2^e\left(\frac{1}{\log _e x}-\frac{1}{\left(\log _e x\right)^2}\right) d x=e-2 \log _2 e
\]
Reason (R)
\[
\int_a^b e^x\left(f(x)+f^{\prime}(x)\right) d x=e^b f(b)-e^a f(a)
\]AP EAMCET 2022 Medium - If a polygon of \(n\) sides has 275 diagonals, then \(n\) is equal toAP EAMCET 2007 Easy
- If the lengths of the tangents drawn from the point \((1,2)\) to the circles
\[
x^2+y^2+x+y-4=0
\]
and \(3 x^2+3 y^2-x-y-\lambda=0\) are in the ratio \(3: 4\), then \(\lambda\) is equal toAP EAMCET 2021 Easy - \(x^2+y^2+2 x+4 y-20=0\) and \(x^2+y^2+6 x-8 y+10=0\) are the given circles. Which one of the following is correct?AP EAMCET 2018 Medium
- The solution of \(\frac{d y}{d x}=\left(\frac{x}{y}\right)^{-1 / 3}\) isAP EAMCET 2002 Medium
- A line \(L\) passes through the points \((1,2,-3)\) and \((3,3-1)\) and a plane \(\pi\) passes through the points \((2,1,-2),(-2,-3,6)\), \((0,2,-1)\). If \(\theta\) is the angle between the line L and plane \(\pi\), then \(27 \cos ^2 \theta=\)AP EAMCET 2024 Medium
More PYQs from AP EAMCET
- If \(f: R \rightarrow R\) is defined by
\[
f(x)=\left\{\begin{array}{cc}
\frac{\cos 3 x-\cos x}{x^2}, & \text { for } x \neq 0 \\
\lambda & , \text { for } x=0
\end{array}\right.
\]
and if \(f\) is continuous at \(x=0\), then \(\lambda\) is equal toAP EAMCET 2008 Hard - Match the pollutant in List I with its maximum permissible limit in drinking water given in List II
\(\begin{array}{|l|l|l|l|}\hline & \text{List-I} & & \text{List-II} \\ \hline \text{A.} & \text{Lead} & \text{I} & 500 \text{ ppm} \\ \hline \text{B.} & \text{Sulphate} & \text{II} & 50 \text{ ppm} \\ \hline \text{C.} & \text{Nitrate} & \text{III} & 50 \text{ ppb} \\ \hline\end{array}\)
Correct answer isAP EAMCET 2024 Easy - A resistor has bands with colours orange, green, silver and gold. Then, the resistance of the resistor isAP EAMCET 2018 Easy
- The direction cosines of the line of intersection of the planes \(x+2 y+z-4=0\) and \(2 x-y+z-3=0\) areAP EAMCET 2024 Easy
- An artificial satellite of mass is moving along an elliptical path around the earth. The areal velocity of the satellite is proportional toAP EAMCET 2018 Easy
- The number of values of for which the pair of lines represented by are at right angles to each other, isAP EAMCET 2019 Easy