Quadratic EquationHard
Question
How many solutions does the system of equations $|x| + |y| = 1,x^{2} + y^{2} = a^{2}$ possess depending on ' $a$ '?
Options
A.if $|a| < \frac{1}{\sqrt{2}}$
B.0 if $|a| > 1$
C.4 if $|a| = \frac{1}{\sqrt{2}},1$
D.8 if $\frac{1}{\sqrt{2}} < |a| < 1$
Solution
$|a| = sin\frac{\pi}{4} = \frac{1}{\sqrt{2}}$
Number of solutions
$$= \left\{ \begin{matrix} 4 & \text{~if~} & a = \left\{ \frac{1}{\sqrt{2}}, - \frac{1}{\sqrt{2}}, - 1,1 \right\} \\ 8 & \text{~if~} & a \in \left( - 1, - \frac{1}{\sqrt{2}} \right) \cup \left( \frac{1}{\sqrt{2}},1 \right) \\ 0 & \text{~if~} & a \in ( - \infty, - 1) \cup \left( - \frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right) \cup (1,\infty) \end{matrix} \right.\ $$
Create a free account to view solution
View Solution FreeMore Quadratic Equation Questions
If roots of quadratic equation ax2 + bx + c = 0 are α and β then symmetric expression of its roots is -...Let x satisfy the equation $\frac{\sqrt{a} + \sqrt{x - b}}{\sqrt{b} + \sqrt{x - a}} = \sqrt{\frac{a}{b}},a,b > 0$, th...The imaginary roots of the equation (x2 + 2)2 + 8x2 = 6x (x2 + 2) are -...Let $M = 3x^{2} - 8xy + 9y^{2} - 4x + 6y + 13$, where $x,y \in R$, then...If α and β are roots of 2x2 − 7x + 6 = 0, then the quadratic equation whose roots are is-...