Question

if the line x/a+y/b =1 be a tangent to xy =c square then​

Answer 1

Given: x/a+y/b =1 and curves are x = ct and y = c/t

To find: value of a and b?

Solution:

• Now we have given xy = c²

• Let tangent at point (x1, y1) be: xy1 + yx1 = 2c²

• At general, let x1 = ct and y1 = c/t and put it in above equation, we get:

            x(c/t) + y(ct) = 2c²

            x/t + yt = 2c

• So the slope of tangent is: -(coeff of x) / coeff of y

            m = -(1/t) / t

            m = -1/t² < 0

• Now given line is x/a + y/b = 1 is tangent for xy = c², but slope of tangent should always be less that zero.

• So m = -1/a  /  1/b < 0

            -b/a < 0

            b/a > 0

• Now there becomes two cases: either both are greater than 0 or both are less than 0.

• So value of a>0 and b>0 or a<0 and b<0.

Answer:

          So value of a>0 and b>0 or a<0 and b<0.