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Byju's Answer
Standard XII
Mathematics
Equation of Tangent at a Point (x,y) in Terms of f'(x)
Find the equa...
Question
Find the equation of the tangent to the curve x
2
+ 3y − 3 = 0, which is parallel to the line y = 4x − 5.
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Solution
Suppose (x
1
, y
1
) be the point of contact of tangent.
We can find the slope of the given line by differentiating the equation w.r.t x
So, Slope of the line = 4
Since
,
x
1
,
y
1
lies
on
the
curve
.
Therefore
,
x
1
2
+
3
y
1
-
3
=
0
.
.
.
1
Now
,
x
2
+
3
y
-
3
=
0
⇒
2
x
+
3
d
y
d
x
=
0
⇒
d
y
d
x
=
-
2
x
3
Slope of tangent,
m
=
d
y
d
x
x
1
,
y
1
=
-
2
x
1
3
Given that tangent is parallel to the line, So
Slope of
tangent
,
m
= slope of the given line
-
2
x
1
3
=
4
⇒
x
1
=
-
6
36
+
3
y
1
-
3
=
0
(From (1))
⇒
3
y
1
=
-
33
⇒
y
1
=
-
11
x
1
,
y
1
=
-
6
,
-
11
Equation of
tangent
is,
y
-
y
1
=
m
x
-
x
1
⇒
y
+
11
=
4
x
+
6
⇒
y
+
11
=
4
x
+
24
⇒
4
x
-
y
+
13
=
0
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0
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