Question
The line $\mathrm{x}-\mathrm{y}+2 \mathrm{c}=0$ intersects the director circle of $\mathrm{x}^{2}+\mathrm{y}^{2}=\mathrm{a}^{2},(\mathrm{a}>0)$ in two real points if(a) $c+a<0$(b) $c+a>0$(c) $c-a<0$(d) $c-a>0$
Step 1
Step 1: The given line is $x - y + 2c = 0$ and the director circle is $x^2 + y^2 = a^2$ where $a > 0$. Show more…
Show all steps
Your feedback will help us improve your experience
Saurabh Kumar Gupta and 74 other Precalculus educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The line $y=m x+c$ and the circle $x^{2}+y^{2}=a^{2}$ do not intersect if (a) $a=\frac{|c|}{\sqrt{1+m^{2}}}$ (b) $\mathrm{a}<\frac{|\mathrm{c}|}{\sqrt{1+\mathrm{m}^{2}}}$ (c) $a>\frac{|c|}{\sqrt{1+m^{2}}}$ (d) $a c=\sqrt{1+m^{2}}$
The locus of the centre of a circle which passes through the point $(0,0)$ and cuts off a length $2 b$ from the line $x$ $=c$, is (A) $y^{2}+2 c x=b^{2}+c^{2}$ (B) $x^{2}+c x=b^{2}+c^{2}$ (C) $y^{2}+2 c y=b^{2}+c^{2}$ (D) none of these
If one of the circles $x^{2}+y^{2}+2 a x+c=0$ and $x^{2}+y^{2}+$ $2 b x+c=0$ lies within the other, then (A) $a b<0$ (B) $a b>0$ (C) $c \leq 0$ (D) $c>0$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD