4 months ago

The circle C has equation[tex](x - 6)^{2} + (y - 5)^{2} = 17[/tex]The lines L1 and L2 are each a tangent to the circle and intersect at the point (0, 12). Find the equations of L1 and L2, giving your answers in the form y=mx+c.

Accepted Solution

Answer:[tex]y=-4x+12\\y =-0.421x+12[/tex]Step-by-step explanation:The lines through (0,12) would have equation of the formy = mx+12If this is tangent, the distance of centre from the tangent = radius of the circleDistance of (6,5) ie centre from tangent line is[tex]\frac{6m+7}{\sqrt{1+m^2} } =\sqrt{17} \\(6m+7)^2 = 17(1+m^2)\\[/tex][tex]36m^2+84m+49 =17+17m^2\\19m^2+84m+32=0[/tex]m=-4,-0.421Hence tangents are[tex]y=-4x+12\\y =-0.421x+12[/tex]

scooplane

scooplane

The circle C has equation[tex](x - 6)^{2} + (y - 5)^{2} = 17[/tex]The lines L1 and L2 are each a tangent to the circle and intersect at the point (0, 12). Find the equations of L1 and L2, giving your answers in the form y=mx+c.

scooplane

scooplane

The circle C has equation[tex](x - 6)^{2} + (y - 5)^{2} = 17[/tex]The lines L1 and L2 are each a tangent to the circle and intersect at the point (0, 12). Find the equations of L1 and L2, giving your answers in the form y=mx+c. ​

The circle C has equation[tex](x - 6)^{2} + (y - 5)^{2} = 17[/tex]The lines L1 and L2 are each a tangent to the circle and intersect at the point (0, 12). Find the equations of L1 and L2, giving your answers in the form y=mx+c.