AP EAMCET · Maths · Circle
If a circle \(S\) passing through the points \(A(1,2)\) and \(B(2,1)\) has its centre \(\mathrm{C}\) located in the third quadrant at a distance of \(\frac{7}{\sqrt{2}}\) units from \(\mathrm{AB}\), then the point \(\mathrm{P}(1,-2)\)
- A lies inside the circle \(\mathrm{S}\)
- B lies outside the circle \(\mathrm{S}\)
- C lies on the circle \(\mathrm{S}\)
- D lies on the line \(\mathrm{AB}\)
Answer & Solution
Correct Answer
(A) lies inside the circle \(\mathrm{S}\)
Step-by-step Solution
Detailed explanation
Now, \(\begin{aligned} & \mathrm{AP}=\frac{1}{2} \sqrt{1^2+(-1)^2}=\frac{1}{\sqrt{2}} \\ & \text { and } \mathrm{PC}=\frac{7}{\sqrt{2}} \\ & \text { so } \mathrm{AC}=\sqrt{\left(\frac{1}{\sqrt{2}}\right)^2+\left(\frac{7}{\sqrt{2}}\right)^2}=5 \end{aligned}\) Now,…
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 \(\theta\) is an acute angle, \(\cos h x=K\) and \(\sin h x=\tan \theta\), then \(\sin \theta=\)AP EAMCET 2024 Medium
- If \((x-i y)^{1 / 3}-a-i b\), then the value of \(\frac{x}{2 a}+\frac{y}{2 b}\) isAP EAMCET 2022 Medium
- If \(\mathrm{f}: \mathbb{R} \backslash\{0\} \rightarrow \mathbb{R}\) is defined by \(\mathrm{f}(\mathrm{x})=\mathrm{x}+\frac{1}{\mathrm{x}}\), then the value of \((\mathrm{f}(\mathrm{x}))^2=\)AP EAMCET 2023 Easy
- If the mean and variance of a binomial variable \(\mathrm{X}\) are 2.4 and 1.44 respectively, then the parameters \(n\) and \(p\) are respectivelyAP EAMCET 2023 Easy
- \(\int_{1 / 5}^{1 / 2} \frac{\sqrt{x-x^2}}{x^3} d x=\)AP EAMCET 2025 Medium
- If and are such that the function defined by is differentiable everywhere then the ordered pairAP EAMCET 2019 Easy
More PYQs from AP EAMCET
- Identify the statements which are not correct.
a) Copper is refined by Van-Arkel method
b) Zinc is refined by electrolysis method
c) Zirconium is refined by distillation methodAP EAMCET 2017 Easy - If \(\vec{a}, \vec{b}, \vec{c}, \vec{d}\) are position vectors of 4 points such that \(2 \vec{a}+3 \vec{b}+5 \vec{c}-10 \vec{d}=\overrightarrow{0}\) then the ratio in which the line joining \(\vec{c}\) and \(\vec{d}\) divides the line segment joining \(\vec{a}\) and \(\vec{b}\) isAP EAMCET 2024 Easy
- A circular disc of mass 20 kg and radius 1 m is rotating about an axis passing through its center and perpendicular to its plane with an angular velocity of \(2 \mathrm{rad} \mathrm{s}^{-1}\). Then the rotational kinetic energy of the disc isAP EAMCET 2025 Easy
- If \(y=\operatorname{Tan}^{-1}\left(\frac{3 x-x^3}{1-3 x^2}\right)+\operatorname{Tan}^{-1}\left(\frac{7 x}{1-12 x^2}\right)\), then at \(x=0, \frac{d y}{d x}=\)AP EAMCET 2025 Medium
- The number of pairs of consecutive positive even integers such that the sum of their squares is 290 isAP EAMCET 2022 Medium
- A circle \(S\) of radius 2 units lies in the first quadrant and touches both the coordinate axes. The equation of the circle with centre at \((6,5)\) and touching the circle \(S\) externally isAP EAMCET 2019 Medium