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How to study Conic Sections in Class 11, Introduction to Circle, Parabola, Ellipse and Hyperbola, Animation to understand why they are called conic sections, How to derive equation of circle

 NCERT EXERCISE 11.1

In each of the following Exercises 1 to 5, find the equation of the circle with

Question 1. center (0, 2) and radius 2
Question 2. center (–2, 3) and radius 4
Question 3. center $$\left ( \frac{1}{2}, \frac{1}{4} \right )$$ and radius $$\frac{1}{12}$$
Question 4. center (1, 1) and radius $$\sqrt{2}$$
Question 5. center $$(-a, -b)$$ and radius $$\sqrt{a^2-b^2}$$

In each of the following Exercises 6 to 9, find the center and radius of the circles.

Question 6. $$(x+5)^2+(y-3)^2=36$$
Question 7. $$x^2+y^2-4x-8y-45=0$$
Question 8. $$x^2+y^2-8x+10y-12=0$$
Question 9. $$2x^2+2y^2-x=0$$

Question 10. Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose center is on the line $$4x + y = 16$$.
Question 11. Find the equation of the circle passing through the points (2, 3) and (–1, 1) and whose center is on the line $$x – 3y – 11 = 0$$.
Question 15. Does the point (–2.5, 3.5) lie inside, outside or on the circle $$x^2 + y^2 = 25$$?