Quadratic Functions, Equations and Inequalities - Nature of Roots of Quadratic Equations
Quadratic Functions, Equations and Inequalities - Nature of Roots of Quadratic Equations
It is given that the point \(P\left( -5,7 \right)\) lies on the circle \({{y}^{2}}+{{x}^{2}}-ay+2x=8\), where \(a\) is a constant.
- Find the value of \(a\).
- Find the radius and the centre of the circle.
- It is given that the point \(Q\) lies on the circle such that \(PQ\) is the diameter of the circle. Find the equation of the line \(PQ\).
The graph of \(4y=-{{x}^{2}}+bx+9\) intersects \(PQ\) at \(2\) distinct points.
- Find the range of possible values of \(b\).
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Answer:(a) \(a=8\) (b) Centre \((-1,4)\), radius \(5\) (c) \(y=-\frac34x+\frac{13}{4}\) (d) \(b<-7\) or \(b>1\)
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