JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
If a line, \(y=m x+c\) is a tangent to the circle, \((x-3)^{2}+y^{2}=1\) and it is perpendicular to a line \(\mathrm{L}_{1},\) where \(\mathrm{L}_{1}\) is the tangent to the circle, \(\mathrm{x}^{2}+\mathrm{y}^{2}=1\) at the point \(\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right),\) then
- A \(c^{2}-6 c+7=0\)
- B \(c^{2}+6 c+7=0\)
- C \(c^{2}+7 c+6=0\)
- D \(c^{2}-7 c+6=0\)
Answer & Solution
Correct Answer
(B) \(c^{2}+6 c+7=0\)
Step-by-step Solution
Detailed explanation
Slope of tangent to \(\mathrm{x}^{2}+\mathrm{y}^{2}=1\) at \(\mathrm{P}\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\) \(2 \mathrm{x}+2 \mathrm{yy}^{\prime}=\left.0 \Rightarrow \mathrm{m}_{\mathrm{T}}\right|_{\mathrm{P}}=-1\) \(y=m x+c\) is tangent to \((x-3)^{2}+y^{2}=1\)…
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 \(\frac{\cos ^2 48^{\circ}-\sin ^2 12^{\circ}}{\sin ^2 24^{\circ}-\sin ^2 6^{\circ}}=\frac{\alpha+\beta \sqrt{5}}{2}\), where \(\alpha, \beta \in N\), then \(\alpha+\beta\) is equal to ___ .JEE Mains 2026 Easy
- Let \(\alpha, \beta, \gamma\) be the real roots of the equation, \(x ^{3}+ ax ^{2}+ bx + c =0,( a , b , c \in R\) and \(a , b \neq 0)\) If the system of equations (in, \(u,v,w\)) given by \(\alpha u+\beta v+\gamma w=0, \beta u+\gamma v+\alpha w=0\) \(\gamma u +\alpha v +\beta w =0\) has non-trivial solution, then the value of \(\frac{a^{2}}{b}\) isJEE Mains 2021 Hard
- Let \(9 < x_1 < x_2 < \ldots < x_7\) be in an \(A.P.\) with common difference \(d\). If the standard deviation of \(x_1, x_2 \ldots\), \(x _7\) is \(4\) and the mean is \(\overline{ x }\), then \(\overline{ x }+ x _6\) is equal to:JEE Mains 2023 Hard
- \(\sum_{\substack{i, j=0 \\ i \neq j}}^{n}{ }^{n} C_{i}{ }^{n} C_{j}\) is equal toJEE Mains 2022 Hard
- The minimum number of times one has to toss a fair coin so that the probability; of observing at least one head is at least \(90\%\) isJEE Mains 2019 Hard
- If \(\frac{{{}^{n + 2}{C_6}}}{{{}^{n - 2}{P_2}}} = 11\), then \(n\) satisfies the equationJEE Mains 2016 Hard
More PYQs from JEE Mains
- Let \(M\) be the maximum value of the product of two positive integers when their sum is \(66\). Let the sample space \(S=\left\{x \in Z: x(66-x) \geq \frac{5}{9} M\right\}\) and the event \(A=\{ x \in S : x\) is a multiple of \(3\) \(\}\). Then \(P ( A )\) is equal toJEE Mains 2023 Hard
- The equation of a circle is \(\operatorname{Re}\left(z^{2}\right)+2(\operatorname{Im}(z))^{2}+2 \operatorname{Re}(z)=0\), where \(z=x+\) iy. A line which passes through the center of the given circle and the vertex of the parabola, \(x^{2}-6 x-y+13=0,\) has \(y\)-intercept equal to \(.....\)JEE Mains 2021 Hard
- If \(f(x)\) and \(g(x)\) are two polynomials such that the polynomial \(P ( x )=f\left( x ^{3}\right)+ xg \left( x ^{3}\right)\) is divisible by \(x^{2}+x+1,\) then \(P(1)\) is equal to ....... .JEE Mains 2021 Hard
- If \(\left( {2 + \sin x} \right)\frac{{dy}}{{dx}} + \left( {y + 1} \right)\cos x = 0\) and \(y\left( 0 \right) = 1\) then \(y\left( {\frac{\pi }{2}} \right) = \) . . . .JEE Mains 2017 Hard
- A tangent line \(\mathrm{L}\) is drawn at the point \((2,-4)\) on the parabola \(\mathrm{y}^{2}=8 \mathrm{x}\). If the line \(\mathrm{L}\) is also tangent to the circle \(x^{2}+y^{2}=a\), then \('a'\) is equal to .... .JEE Mains 2021 Hard
- Let \(n \in N\) and \([x]\) denote the greatest integer less than or equal to \(x\). If the sum of \((n+1)\) terms \({ }^{n} C_{0}, 3 .{ }^{n} C_{1}, 5 .{ }^{n} C_{2}, 7 .{ }^{n} C_{3}, \ldots\) is equal to \(2^{100} \cdot 101\), then \(2\left[\frac{n-1}{2}\right]\) is equal to \(....\)JEE Mains 2021 Hard