AP EAMCET · Maths · Circle
Suppose the angle between the tangents drawn from \((0,0)\) to the circle \((x+\lambda)^2+(y+1)^2=\lambda^2\) is \(\frac{\pi}{2}\). Then, \(\lambda\) satisfies
- A \(\lambda^2=1\)
- B \(\lambda=0\)
- C \(\lambda^2=4\)
- D \(\lambda^2=9\)
Answer & Solution
Correct Answer
(A) \(\lambda^2=1\)
Step-by-step Solution
Detailed explanation
\((x+\lambda)^2+(y+1)^2=\lambda^2\) \(\begin{aligned} & C \equiv(-\lambda,-1) r=\lambda \\ & \angle C O P=\frac{90^{\circ}}{2}=45^{\circ}\end{aligned}\) \(\begin{aligned} \therefore \quad O P & =C P=\lambda \\ O C & =\sqrt{\lambda^2+1}\end{aligned}\) In…
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
- \[
\text { }\left[\begin{array}{ccc}
1 & 2 & 3 \\
-1 & 1 & 2 \\
3 & 0 & 2
\end{array}\right]
\]
\[
\left|\begin{array}{ll}
2022 & 2024 \\
2021 & 2023
\end{array}\right|
\]
is equal toAP EAMCET 2021 Hard - If \(\frac{y}{x} \cos ^4 \alpha+\frac{x}{y} \sin ^4 \alpha=2 \sin ^2 \alpha \cdot \cos ^2 \alpha\), then \(\frac{d y}{d x}=\)AP EAMCET 2022 Hard
- If \(\sec \theta+\tan \theta=\frac{1}{3}\), then the quadrant in which \(2 \theta\) lies isAP EAMCET 2024 Easy
- If \(x=\sec \theta-\cos \theta, y=\sec ^n \theta-\cos ^n \theta\) then \(\frac{d y}{d x}=\)AP EAMCET 2018 Medium
- If \(a, b\) and \(c\) are real numbers such that \(a^2+b^2+c^2-a b-b c-a c \leq 0\), then
\[
\left|\begin{array}{ccc}
(a-b+1)^5 & b^7-c^7 & c^9-a^9 \\
a^{11}-b^{11} & (b-c+2)^3 & c^{13}-a^{13} \\
a^{15}-b^{15} & b^{17}-c^{17} & (c-a+3)^1
\end{array}\right|=
\]AP EAMCET 2021 Medium - AP EAMCET 2020 Medium
More PYQs from AP EAMCET
- Simultaneously, from the top of a tower, when ball- 1 is thrown horizontally and ball- 2 is just dropped, in the absence of air resistance which among the following options is correct?AP EAMCET 2020 Medium
- How many unit cells are present in a cube shaped ideal crystal of \(\mathrm{NaCl}\) of mass lg?AP EAMCET 2021 Medium
- \(A\) and \(B\) are two independent events of a random experiment and \(P(A)>P(B)\).
If the probability that both \(A\) and \(B\) occur is \(\frac{1}{6}\) and neither of them occurs is \(\frac{1}{3}\), then the probability of the occurance of \(B\) isAP EAMCET 2025 Medium - Which of the following exhibit ionization isomerism ?
I) \(\left[\mathrm{Cr}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right] \mathrm{Cl}\)
II) \(\left[\mathrm{Ti}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{Cl}\right]\left(\mathrm{NO}_3\right)_2\)
III) \(\left[\mathrm{Pt}(\mathrm{en})\left(\mathrm{NH}_3\right) \mathrm{Cl}\right] \mathrm{NO}_3\)
IV) \(\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4\left(\mathrm{NO}_3\right)_2\right] \mathrm{NO}_3\)AP EAMCET 2025 Medium - Calculate the molar ratio of a weak acid \(\mathrm{H} A\left(K_a=10^{-6}\right)\) and its salt with strong base, so that the \(\mathrm{pH}\) of buffer solution is 6 .AP EAMCET 2020 Hard
- Identify incorrectly matched set from the followingAP EAMCET 2023 Easy