AP EAMCET · Maths · Circle
If the line through the point \(P(5,3)\) meets the circle \(x^2+y^2-2 x-4 y+\alpha=0\) at \(\mathrm{A}(4,2)\) and \(\mathrm{B}\left(x_1, y_1\right)\), then \(P A \cdot P B\) is equal to
- A 6
- B 12
- C 9
- D 8
Answer & Solution
Correct Answer
(D) 8
Step-by-step Solution
Detailed explanation
Line through \(P(5,3)\) meets the circle \(x^2+y^2-2 x-4 y+\alpha=0 \text { at } A(4,2) \text { and } B\left(x_1, y_1\right)\) \(\therefore A(4,2)\) lies on the circle \(\Rightarrow 16+4-8-8+\alpha=0 \Rightarrow \alpha=-4\) Eq. of circle becomes \(x^2+y^2-2 x-4 y-4=0\) Also,…
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 \(\sec (\theta+\alpha), \sec \theta, \sec (\theta-\alpha)\) are in arithmetic progression, then \(\cos \theta \cdot \sec \frac{\alpha}{2}=\)
2.
3. \pm 2
www. android.universityupdates.in \(\mid\) www.universityupdates.in \(\mid\) www. ios.universityupdates.in
www.android.previousquestionpapers.com | www.previousquestionpapers.com | www.ios.previousquestio 4.AP EAMCET 2018 Medium - If \(\alpha, \beta\) are the roots of \(x^2+b x+c=0, \gamma, \delta\) are the roots of \(x^2+b_1 x+c_1=0\) and \(\gamma < \alpha < \delta < \beta\), then \(\left(c-c_1\right)^2 < \)AP EAMCET 2019 Hard
- If a circle \(S\) with radius 5 touches the circle \(x^2+y^2-6 x-4 y-12=0\) at \((-1,-1)\), then the length of the tangent from the centre of the circle \(S\) to the given circle isAP EAMCET 2018 Medium
- If \(l_1, m_1, n_1\) and \(l_2, m_2, n_2\) are direction cosines of \(\mathbf{O A}\) and \(O B\) such that \(\angle A O B=\theta\), where \(O\) is the origin, then the direction cosines of the internal angular bisector of \(\angle A O B\) areAP EAMCET 2019 Medium
- The straight line passing through \((-1,1)\) and remaining parallel to the line common to the pairs of lines provided by \(6 x^2-x y-12 y^2=0\) and \(15 x^2+14 x y-8 y^2=0\), isAP EAMCET 2022 Medium
- If \(A=\left[\begin{array}{lll}83 & 74 & 41 \\ 93 & 96 & 31 \\ 24 & 15 & 79\end{array}\right]\), then \(\operatorname{det}\left(A-A^{\mathrm{T}}\right)=\)AP EAMCET 2024 Easy
More PYQs from AP EAMCET
- Figure shows a straight wire placed between the pole pieces of a magnet. Induced emf will be developed across the ends of the wire
when it is moved towards.
AP EAMCET 2021 Medium - Three vessels \((A, B, C)\) contain \(\mathrm{H}_2 \mathrm{O}_2\) solution. In vessel \(A, 500 \mathrm{~mL}\) of \(10 \mathrm{vol} \mathrm{H}_2 \mathrm{O}_2\) is present. \(100 \mathrm{~mL}\) of \(30 \mathrm{vol} \mathrm{H}_2 \mathrm{O}_2\) is present in vessel \(B\). Vessel \(C\) is filled with \(250 \mathrm{~mL}\) of \(2 \mathrm{M} \mathrm{H}_2 \mathrm{O}_2\). The weight (in \(\mathrm{g}\) ) of \(\mathrm{H}_2 \mathrm{O}_2\) present in these vessels follows the orderAP EAMCET 2019 Medium
- Consider the cell reaction, at 300 K
\(\mathrm{A}(s)+\mathrm{B}^{2+}(a q) \rightleftharpoons \mathrm{A}^{2+}(a q)+\mathrm{B}(s)\)
Its \(\mathrm{E}^{\circ}\) is 1.0 V . The \(\Delta_{\mathrm{r}} \mathrm{H}^{\circ}\) of the reaction is \(-163 \mathrm{~kJ} \mathrm{~mol}^{-1}\). What is \(\Delta_{\mathrm{r}} \mathrm{S}^{\circ}\) (in J K\({ }^{-1}\) ) of the reaction?
\(\left(\mathrm{F}=96500 \mathrm{C} \mathrm{~mol}^{-1}\right)\)AP EAMCET 2024 Medium - If \(\int \frac{1}{1-\cos x} d x=\tan \left(\frac{x}{\alpha}+\beta\right)+c\), then one of the values of \(\frac{\pi \alpha}{4}-\beta\) isAP EAMCET 2024 Easy
- If \(\log 2=a, \log 3=b, \log 7=c\) and \(6^x=7^{x+4}\) then \(x\) is equal toAP EAMCET 2002 Easy
- The number of elements in the set \(S=\{x \in \mathbb{Z}\) : \(x^2-7 x+6 \leq 0\) and \(\left.x^2-3 x>0\right\}\) isAP EAMCET 2023 Medium