Question

Circle S1 : x² + y² = 1, S2: x² + y² -6x -6y+17 =0 has
(A) 4 common tangents
(B) 2 direct common tangents
(C) 2 transverse common tangents
(D) length of direct common tangents is 3√2​

Answer 1

Answer:

Go through Part-1 carefully, and make a list of as many words as you can find that indicate movement of different kinds. (There is one word that occurs repeatedly-count how many times!) Put them into three categories.

fast movement slow movement neither slow nor fast

Can you explain why there are many words in one column and not in the

others?

Fill in the blanks in the sentences below (the verbs given in brackets will give you a clue).

Answer 2

Answer:

{\underline{\underline{\maltese\textbf{\textsf{\red{Question}}}}}}✠Question

: \implies{\sf\bigg({\dfrac{x}{2} - 6}\bigg) = \bigg({8 - \dfrac{2x}{3}} \bigg)}:⟹(2x−6)=(8−32x)

\begin{gathered}\end{gathered}

{\underline{\underline{\maltese\textbf{\textsf{\red{Solution}}}}}}✠Solution

: \implies{\sf\bigg({\dfrac{x}{2} - 6}\bigg) = \bf\bigg({8 - \dfrac{2x}{3}} \bigg)}:⟹(2x−6)=(8−32x)

{: \implies{\sf\bigg({\dfrac{x - (6 \times 2)}{2}}\bigg) = \bf\bigg({\dfrac{(8 \times 3) - 2x}{3}} \bigg)}}:⟹(2x−(6×2))=(3(8×3)−2x)

{: \implies{\sf\bigg({\dfrac{x - 12}{2}}\bigg) = \bf\bigg({\dfrac{24 - 2x}{3}} \bigg)}}:⟹(2x−12)=(324−2x)

By cross multiplication

: \implies\sf{3(x - 12) = \bf{2(24 - 2x)}}:⟹3(x−12)=2(24−2x)

: \implies\sf{3x - 36 = \bf{48 - 4x}}:⟹3x−36=48−4x

: \implies\sf{4x - 3x = \bf{48 -36}}:⟹4x−3x=48−36

: \implies\sf{x = \bf{12}}:⟹x=12

{\dag{\underline{\boxed{\sf{x =12}}}}}†x=12

Hence, The value of x is 12.

\begin{gathered}\end{gathered}

{{\underline{\underline{\maltese\textbf{\textsf{\red{Verification}}}}}}}✠Verification

: \implies{\sf\bigg({\dfrac{x}{2} - 6}\bigg) = \bf\bigg({8 - \dfrac{2x}{3}} \bigg)}:⟹(2x−6)=(8−32x)

Substituting the value of x

: \implies{\sf\bigg({\dfrac{12}{2} - 6}\bigg) = \bf\bigg({8 - \dfrac{2