Mathematics

The shortest distance between the line $y=x$ and the curve $y^2=x-2$ is :

$\dfrac{7}{4\sqrt{2}}$

SOLUTION
we have ,$2y.\dfrac{dy}{dx}=1\Rightarrow\dfrac{dy}{dx}]_{P(2+t^2,t)}=\dfrac{1}{2t}=1$
$\Rightarrow t=\dfrac{1}{2}$
$\therefore P\left(\dfrac{9}{4},\dfrac{1}{2}\right)$
So, shortest distance
$=\dfrac{\left|\dfrac{9}{4}-\dfrac{2}{4}\right|}{\sqrt{2}}=\dfrac{7}{4\sqrt{2}}$

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!

Single Correct Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86

Realted Questions

Q1 Single Correct Medium
In the figure above, two line segments meet at a point on line $l$. Find the value of $x$.
• A. $60$
• B. $90$
• C. $15$
• D. $45$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Subjective Medium
In the adjoining figure, identify the pair of corresponding angles.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Subjective Medium
Find the value of unknown x in the following diagram.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Subjective Medium
In the given figure, $\angle ABD =54^o$ and $\angle BCD=43^o$, calculate
$\angle ACD$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Single Correct Medium
The complementary angle of $\displaystyle 30^{\circ}$ is:
• A. $\displaystyle 90^{\circ}$
• B. $\displaystyle 150^{\circ}$
• C. none of these
• D. $\displaystyle 60^{\circ}$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020