recalling the general form of a circle as
(i) It is a quadratic equation in both x and y.
(ii) Coefficient of = Coefficient of .
(iii) There is no term containing xy i.e., the coefficient of xy is zero.
(iv) radius is
To satisfy (i) and (ii) condition we have
To satisfy (iii) condition we have
To satisfy (iv) and as we cant have neagtive sign in root so
is a circle. The points (0, 0) and ( 1, 8) lie
point of intersection is (0,0) and (1,1). Hence by using the distance formula
=
Given 9x2 - 16y2 = 144
Dividing throughout by 144 we get,
- = 1
This implies a2 = 16 and b2 = 9
e = =
Given equation is 3x2 + 4y2 = 24
dividing throught by 24 we get,
+ = 1
This implies a2 = 8 and b2 = 6
e = =
The contion for a line to be a tangent to the parabola is y = mx +
From the given equation of the parabola we infer that a = 1 and from the equation of the line c = 1
Therefore m = a/c = 1