show y=3x-5 is tangent to x^2 + y^2 +2x -4y - 5 = 0 and the point where they touch
y=3x-5x^2 + (3x-5)^2 + 2x - 4(3x-5) - 5 = 0x^2 + 9x^2 -30x +25 + 2x -12x + 20 - 5 = 010x^2 -40x + 40 = 010 (x^2 - 4x +4) = 010(x - 2)^2 = 0x=2implies one point of contact, therefore tangenty = 3x - 5y = 6 -5 = 1
RM
Related Maths Scottish Highers answers
All answers ▸A circle has equation x^2+y^2+6x+10y-7=0. Find the equation of the tangent line through the point on the circle (-8,-1).
Find the stationery points of x^3 + 3x^2 - 24x + 7 and determine whether the slope is increasing or decreasing at x=3.
A circle has equation x^2+y^2-8x+10y+41=0. A point on the circle has coordinates (8,-3). Find the equation of the tangent to the circle passing through this point.
Calculate the rate of change of d(t )=2/(3t), t ≠ 0, when t=6.