Question

The staight line y=3x + 5 does not meet the curve x^2-kxy-3=0. Show that 25k^2 - 36k +12 < 0

Answer 1

y = 3x + 5,....(1)

Substitute this in the curve x² - kxy -3 = 0,

x² - k(x)(3x+5) - 3 =0

⇒x² - 3kx² - 5kx -3 = 0

⇒x²(1-3k) - 5kx - 3 = 0

Since the line and the curve do not meet they should not have same coordinates. Hence the quadratic expression above must not have roots or its discriminant must be zero.

i.e Δ < 0

⇒(-5k)² - 4(1-3k)(-3) < 0

⇒25k² + 12  -36k < 0

Hence 25k² - 36k +12 < 0

Answer 2

Answer:

HOPE THE ATTACHMENT HELPS YOU