Failed to connect to MySQL: Access denied for user 'examnext_online'@'localhost' (using password: YES) If two curves `c_1` x = `y^2` and `c_2` xy = k cut at right angles, then find the value of k. - Sarthaks eConnect

If two curves `c_1` : x = `y^2` and `c_2` : xy = k cut at right angles, then find the value of k.

`+-1/(2sqrt2)`

`+-1/2`

`+-1/4`

`+-1/(sqrt2)`

Solution

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x = `y^2` .............(i)

xy = k .............(ii)

Solving curves `y^2 = k =>y = k^(1/3) => x = k^(2/3)` Therefore, the point of intersection is `(k^(2/3), k^(1/3))`.