1708
1) What is the smallest distance between the point(-2,-2) and a point on the circumference of the circle given by
(x - 1)2 + (y - 2)2 = 4?
A) 3
B) 4
C) 5
D) 6
E) 7
2)Find a negative value of k so that the graph of y = x2 - 2x + 7 and the graph of y = kx + 5 are tangent?
A) - 4√2
B) - 2 - 2√2
C) - 2
D) - √2
E) - 2 + √2
-
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4 Answers
1708
\hspace{-16}$If Line $\mathbf{y=kx+5}$ is tangent to the ciuve at point\\\\ $\mathbf{y=x^2-2x+7}\;,$ Then Slope of These two curves at point \\\\ $\mathbf{\left(x_{1},y_{1}\right)}$ are equal. \\\\ So $\mathbf{{2x-2}|_{x_{1},y_{1}}={k}|_{x_{1},y_{1}}}$\\\\ So $\mathbf{2x_{1}-2=k\Leftrightarrow x_{1}=\frac{k+2}{2}}$\\\\ And $\mathbf{\left(x_{1},y_{1}\right)}$ also lie on $\mathbf{y=kx+5}$ and $\mathbf{y=x^2-2x+7}$\\\\ So $\mathbf{x^2_{1}-2x_{1}+7=kx_{1}+5}$\\\\ $\mathbf{\left(\frac{k+2}{2}\right)^2-2.\left(\frac{k+2}{2}\right)+7=k.\left(\frac{k+2}{2}\right)+5}$\\\\ After Solving We Get\\\\ $\mathbf{\boxed{\bold{k=\left(-2-2.\sqrt{2}\right)}}}$\\\\
