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nikhil arora Grade: 12
`        if  x+y=k touches the parabola y=x-x² then k=?`
7 years ago

## Answers : (2)

Chetan Mandayam Nayakar
312 Points
```										Dear Nikhil,
y=k-x=x-x2, x2-2x+k=0,x=1±√(1-k), y=x-x2, dy/dx=1-2x= -1±√(1-k)=-1 because slope of x+y=k=-1, therefore,k=1
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7 years ago
vikas askiitian expert
510 Points
```										x+y=k............1
y=x-x2 ...............2
from 1 and 2
k-x=x-x2
x2 -2x+k=0 .............3
if line touches the parabola then there will be only one point of contact of line with parabola..
for this condition ,in eq 3 there should be only one value of x
so discriminant =0
b2 =4ac
4k=4
k=1
```
7 years ago
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