AP EAMCET · Maths · Circle
If the lines joining the origin to the points of intersection of \(y=m x+1\) and \(x^2+y^2=1\) are perpendicular, then .........
- A \(m=-1\) only
- B \(m=1\) only
- C \(m= \pm 1\)
- D \(m=0\)
Answer & Solution
Correct Answer
(C) \(m= \pm 1\)
Step-by-step Solution
Detailed explanation
Equation of line joining origin to the points of intersection of \(y=m x+1\) and \(x^2+y^2=1\) is \[ \begin{array}{rlrl} x^2+y^2 & =(y-m x)^2 \\ \Rightarrow & & x^2+y^2 & =y^2-2 m x y+m^2 x^2 \\ \Rightarrow & & \left(1-m^2\right) x^2+2 m x y & =0 \end{array} \] The line are…
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
- Given, \(\sin x=\sum_{n=1}^{\infty}(-1)^{n-1} \frac{x^{2 n-1}}{(2 n-1) !}\). If the function \(f(x)\) given by \(f(x)=\frac{\cos (\sin x)-\cos x}{x^4}(x \neq 0)\) and \(f(0)=k\), is continuous at \(x=0\), then \(k=\)AP EAMCET 2019 Hard
- The product of the distinct \((2 n)\) th roots of \(1+i \sqrt{3}\) is equal to :AP EAMCET 2006 Hard
- The curves \(y=x^2-1, y=8 x-x^2-9\)AP EAMCET 2022 Easy
- If the line \(y=2 x+k\) is normal to the parabola \(y^2=4 x\), then \(k=\)AP EAMCET 2020 Medium
- Let \(\mathrm{L}\) be the line passing through the points \(\hat{\mathrm{i}}-9 \hat{\mathrm{k}}\) and \(7 \hat{j}+\hat{k}\) and \(\pi\) be the plane passing through the point \(6 \hat{i}+\hat{j}\) and perpendicular to the vector \(\hat{i}+\hat{j}+\hat{k}\). If \(\theta\) is the angle between \(\mathrm{L}\) and \(\pi\), then \(\sin \theta=\)AP EAMCET 2023 Medium
- If the line touches the curve thenAP EAMCET 2020 Easy
More PYQs from AP EAMCET
- The lines \((a+2 b) x+(a-3 b) y=a-b\) for different values of \(a\) and \(b\) pass through the fixed point whose coordinates areAP EAMCET 2021 Easy
- In \(\triangle \grave{A B C}\), if \(4 r_1=5 r_2=6 r_3\), then \(\sin ^2 \frac{A}{2}+\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}=\)AP EAMCET 2024 Hard
- If a function \(\mathrm{f}(\mathrm{x})\) defined by
\(f(x)=\left\{\begin{array}{c}a x^2+b x+c, x \leq-1 \\ 2 x^2+4 x+1,-1 < x < 1 \\ c x^2+b x+a, x \geq 1\end{array}\right.\)
is continuous on \(\mathbb{R}\), and \(\lim _{x \rightarrow \frac{3}{2}} f(x)=14\), then
\(\lim _{x \rightarrow-2} f(x)=\quad x \rightarrow \frac{3}{2}\)AP EAMCET 2023 Medium - Isothermal process has non-linear graph between:AP EAMCET 2021 Easy
- The concentration of an organic compound in chloroform is \(6.15 \mathrm{~g}\) per \(100 \mathrm{~mL}\) of solution. A portion of this solution in a \(5 \mathrm{~cm}\) polarimeter tube causes an observed rotation of \(-1.2^{\circ}\). What is the specific rotation of the compound?AP EAMCET 2009 Medium
- Potential difference between the points \(P\) and \(Q\) in the circuit shown is
AP EAMCET 2020 Easy