The equation of the tangent to the curve $6y = 7 - x^3$ at the point $(1, 1)$ is:
- A$2x + y = 3$
- B$x + 2y = 3$
- C$x + y = -1$
- D$x + y + 2 = 0$
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For the circle $C$ with the equation $x^2+y^2-16x-12y+64=0$,match the List-$I$ with the List-$II$ given below.
List-$I$ List-$II$ $(i)$ The equation of the polar of $(-5, 1)$ with respect to $C$ $(A)$ $y = 0$ $(ii)$ The equation of the tangent at $(8, 0)$ to $C$ $(B)$ $y = 6$ $(iii)$ The equation of the normal at $(2, 6)$ to $C$ $(C)$ $x + y = 7$ $(iv)$ The equation of the diameter of $C$ through $(8, 12)$ $(D)$ $13x + 5y = 98$ $(E)$ $x = 8$
| List-$I$ | List-$II$ |
| $(i)$ The equation of the polar of $(-5, 1)$ with respect to $C$ | $(A)$ $y = 0$ |
| $(ii)$ The equation of the tangent at $(8, 0)$ to $C$ | $(B)$ $y = 6$ |
| $(iii)$ The equation of the normal at $(2, 6)$ to $C$ | $(C)$ $x + y = 7$ |
| $(iv)$ The equation of the diameter of $C$ through $(8, 12)$ | $(D)$ $13x + 5y = 98$ |
| $(E)$ $x = 8$ |
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