For what values of r would the line x + y = r be tangent to the circ.pdf
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For your argument r For Protectionism come up with 2 arguments to su.pdf
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For what values of r would the line x + y = r be tangent to the circ.pdf
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For what values of r would the line x + y = r be tangent to the circle x2 + y2 = 4? Solution Solve x + y = r for y: y = r - x Substitute in the equation of the circle: x2 + (r - x)2 = 4 Expand: 2 x2 -2 r x + r 2 - 4 = 0 If we solve the above quadratic equation (in x) we will obtain the x coordinates of the points of intersection of the line and the circle. The 2 points of intersection \"become one\" and therefore the line and the circle become tangent if the discriminant D of the quadratic equation is zero. Hence D = (-2r)2 - 4(2)(r2 - 4) = 4(8 - r2) = 0 Solve for r to obtain: r = 2sqrt(2) and r = - 2sqrt(2).
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For what values of r would the line x + y = r be tangent to the circ.pdf
- For what values of r would the line x + y = r be tangent to the circle x2 + y2 = 4? Solution Solve x + y = r for y: y = r - x Substitute in the equation of the circle: x2 + (r - x)2 = 4 Expand: 2 x2 -2 r x + r 2 - 4 = 0 If we solve the above quadratic equation (in x) we will obtain the x coordinates of the points of intersection of the line and the circle. The 2 points of intersection "become one" and therefore the line and the circle become tangent if the discriminant D of the quadratic equation is zero. Hence D = (-2r)2 - 4(2)(r2 - 4) = 4(8 - r2) = 0 Solve for r to obtain: r = 2sqrt(2) and r = - 2sqrt(2)