= 0 – (x2 × 1) + (x × x) = -x2 + x2 = 0
[From eq. (i)] Therefore,The correct option is option (B) .
Centre of the circle on axis is . Equation of the circle having centre on axis an radius unit is ……….(i) Here is the only arbitrary constant, therefore we will differentiate only once. ...
\[\begin{array}{*{35}{l}} \Rightarrow ~x\text{ }{{\left( y ‘\right)}^{2}}~+\text{ }xyy’’\text{ }-\text{ }yy’\text{ }=\text{ }0 \\ \Rightarrow ~xyy’’\text{ }+\text{ }x{{\left( y’...
\[\begin{array}{*{35}{l}} \Rightarrow ~-x\text{ }{{\left( y’ \right)}^{2}}~-\text{ }xyy”\text{ }+\text{ }yy’\text{ }=\text{ }0 \\ \Rightarrow ~xyy”\text{ }+\text{ }x\text{ }{{\left( y’...
\[{{x}^{2}}~=\text{ }4ay\text{ }\ldots \text{ }[equation\text{ }\left( i \right)\]
Solution: assuming (p, 0) be the centre of the circle. Therefore, it touches the y – axis at origin, its radius is p. Since, the equation of the circle with centre (p, 0) and radius (p) is...
Differentiating both sides two times w.r.t. [By eq. (i)]……….(ii) Again differentiating w.r.t. , [By eq. (i)]
Differentiating both sides two times w.r.t. [By eq. (i)]……….(ii) Again differentiating w.r.t. , ……….(iii) Now from eq. (ii), Putting this value of in eq. (iii), ...
DifferentiatING both sides two times w.r.t. ……….(ii) Again differentiating w.r.t. , ……….(iii) Multiplying eq. (i) by 3 and subtracting eq. (ii) from it, we get ……….(iv) Again multiplying eq....
Equation of the family of curves ……….(i) Differentiating both sides two times w.r.t. ……….(ii) Again differentiating w.r.t. , ……….(iii) Putting this value of in eq. (ii), we get ...
Equation of the family of curves ……….(i) Differentiating both sides two times w.r.t. ……….(ii) Again differentiating w.r.t. , Multiplying both sides by , which the required differential...