Suggested languages for you:

Americas

Europe

Problem 3

If the circle \(x^{2}+y^{2}+2 g x+2 f y+c=0\) cuts each of the circles \(x^{2}+y^{2}-4=0\), \(x^{2}+y^{2}-6 x-8 y+10=0\) and \(x^{2}+y^{2}+2 x-4 y-2=0\) at the extremities of a diameter, then : (b) \(g+f=c-1\) (a) \(c=-4\) (d) \(g f=6\) (c) \(g^{2}+f^{2}-c=17\)

Expert verified

The answer is (c) \((g^{2}+f^{2}) - c = 36\)

What do you think about this solution?

We value your feedback to improve our textbook solutions.

- Access over 3 million high quality textbook solutions
- Access our popular flashcard, quiz, mock-exam and notes features
- Access our smart AI features to upgrade your learning

Chapter 1

The circle \(x^{2}+y^{2}-6 x-6 y+9=0\) is rolled on the \(x\)-axis in the positive direction through one complete revolution. Find the equation of the circle in the new position.

Chapter 1

The equation of the circle which touches the axes of co-ordinates and the line \(\frac{x}{3}+\frac{y}{4}=1\) and whose centres lies in the first quadrant is $$ x^{2}+y^{2}-2 \lambda x-2 \lambda y+\lambda^{2}=0 $$ which \(\lambda\) is equal to: (a) 1 (b) 2 (c) 3 (d) 6

Chapter 1

Find the equation of the circles passing through \((-4,3)\) and touching the lines \(x+y=2\) and \(x-y=2\)

Chapter 1

An isosceles right angled triangle, whose sides are \(1,1, \sqrt{2}\) lies entirely in the first quadrant with the ends of the hypotenuse on the co- ordinate axes. If it slides, prove that the locus of its centroid is $$ (3 x-y)^{2}+(x-3 y)^{2}=\frac{32}{9} $$

Chapter 1

If the points \((-2,0),\left(-1, \frac{1}{\sqrt{3}}\right)\) and $(\cos \theta, \sin \theta)\( are collinear, then the number of values of \)\theta \in[0,2 \pi]$ is: (a) 0 (b) 1 (c) 2 (d) infinite

The first learning app that truly has everything you need to ace your exams in one place.

- Flashcards & Quizzes
- AI Study Assistant
- Smart Note-Taking
- Mock-Exams
- Study Planner