Question

What is the envelope of the family of straight lines y = mx +\(\frac{a}{m} \), m is the parameter?

(a) y = 4ax

(b) y^2 = 4ax

(c) x = 4ay

(d) x^2 = 4ay

The question was posed to me in an interview for internship.

Question is from Envelopes topic in section Differential Calculus of Engineering Mathematics

Answer 1

Right choice is (b) y^2 = 4ax

Best explanation: The given equation can be written as m^2x – ym + a = 0 —-> eq(1) is in the form At^2 + Bt + C =0

The envelope is given by B^2 – 4AC = 0 ——> eq(2)

From eq(1), A = x , B = -y , C = a

Putting the values in eq(2),

(-y)^2 – 4(x)(a) = 0

 y^2 = 4ax.