
If $(a, b)$ is point on the circle whose center is on the $x$-axis and which touches the line $x+y=0$ at $(2,-2)$, then the greatest value of a is
A. $4+2\sqrt{2}$
B. $2+2 \sqrt{2}$
C. $4+\sqrt{2}$
D. None of these
Answer
164.4k+ views
Hint: The slope of a line frequently represents the steepness and orientation of the line. It is easy to determine the slope of a straight line between two points by computing the difference between their coordinates, $(x_1,y_1)$ and. $(x_2,y_2)$
Complete step by step solution:
Consider the figure according to the question

Image: Circle
We know that the equation for slope of a line is
$m=\left(y_{2}-y_{1}\right) /\left(x_{2}-x_{1}\right)$
A line that touches a curve or a circle at one point is said to be tangent. The point of tangency is the intersection of the tangent line and the curve.
The line’s slope is $-1$,
$\therefore \angle {COP}=45^{0}$
$\therefore {OP}=2 \sqrt{2}={CP}$
$\therefore {OC}=\sqrt{(2 \sqrt{2})^{2}+(2 \sqrt{2})^{2}}=4$
The circle's point with the highest ${x}$-coordinate is called ${A}$
$\therefore \text{a}=\text{OA }$
$=\text{OC}+\text{CA}$
$=4+2\sqrt{2}$
Option ‘A’ is correct
Note: The point slope form formula can be used to determine a line's equation. The equation of a line with a given point and a given slope is found using the point slope form. This formula can only be used if the slope of the line and a point on the line are known. The slope-intercept form and the intercept form are two additional formulas that can be used to find the equation of a line.
Complete step by step solution:
Consider the figure according to the question

Image: Circle
We know that the equation for slope of a line is
$m=\left(y_{2}-y_{1}\right) /\left(x_{2}-x_{1}\right)$
A line that touches a curve or a circle at one point is said to be tangent. The point of tangency is the intersection of the tangent line and the curve.
The line’s slope is $-1$,
$\therefore \angle {COP}=45^{0}$
$\therefore {OP}=2 \sqrt{2}={CP}$
$\therefore {OC}=\sqrt{(2 \sqrt{2})^{2}+(2 \sqrt{2})^{2}}=4$
The circle's point with the highest ${x}$-coordinate is called ${A}$
$\therefore \text{a}=\text{OA }$
$=\text{OC}+\text{CA}$
$=4+2\sqrt{2}$
Option ‘A’ is correct
Note: The point slope form formula can be used to determine a line's equation. The equation of a line with a given point and a given slope is found using the point slope form. This formula can only be used if the slope of the line and a point on the line are known. The slope-intercept form and the intercept form are two additional formulas that can be used to find the equation of a line.
Recently Updated Pages
Environmental Chemistry Chapter for JEE Main Chemistry

Geometry of Complex Numbers – Topics, Reception, Audience and Related Readings

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Displacement-Time Graph and Velocity-Time Graph for JEE

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

Degree of Dissociation and Its Formula With Solved Example for JEE

Instantaneous Velocity - Formula based Examples for JEE

JEE Main 2025: Conversion of Galvanometer Into Ammeter And Voltmeter in Physics

JEE Advanced 2025 Notes
