Question

Find the co-ordinates of the points where the circle r + y2 - 7x -8y + 12 = 0 meets the
coordinate axes and hence find the intercepts on the axes.
(Hint: Ifa circle intersects a line Lat points A and B. then the length, AB is its intercepts on
the line L)​

Answer 1

Answer:(i) (4,0) , (3,0) , (0,6) , (0,2)

(ii) 1 unit on the x axis, 4 units on the y axis

Step-by-step explanation:

All you have to do for the first part is substituting x = 0 and y = 0 and solving two quadratics to get (at max) 4 intersection points on the axes.

Substituting x = 0, you'd get y^2 - 8y +12 = 0

y^2 - 6y - 2y + 12 = 0

(y-6)(y-2) = 0 .........(i)

Substituting y = 0, you'd get x^2 - 7x + 12 = 0

x^2 - 4x - 3x + 12 = 0

(x-4)(x-3) = 0 ..........(ii)

From equations (i) and (ii), we can say that the coordinates of the point of intersection on the axes would be : (4,0) , (3,0) , (0,6) , (0,2)

From the above points, the length of the intercepts on the x-axis would be 1 unit and the length of the intercept on the y axis would be 4 units

Answer 2

Answer:

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