Given the system of straight lines a(2x+y-3) + b(3x+2y-5) = 0, the  line of the system farthest from the point (4,-3) has the equation?
Options: a) 4x+11y-15=0
b) 7x+y-8=0
c) 4x+3y-7=0
d) 3x-4y+1=0


2 years ago

Share

                                         Hi Suhas,

The given system represents a family of lines passing through the intersection of 2x+y-3=0 and 3x+2y-5=0
These two lines intersect at (1,1).

Now a line throug this system will be the farthest from the point (4,-3) if the line is perpendicular to the line joining (1,1) and (4,-3).
Slope of the line joining (4,-3) and (1,1) is -4/3.
So slope of the required line passing through (1,1) is 3/4.

So the eqn of the line will be 3x-4y+7=0 (there is no option in the question, please check your choice D).

Regards,

2 years ago
                                        Hi Suhas,

Sorry. A silly mistake in the last step.
Eqn of line through (1,1) and having slope as 3/4 will be 3x-4y+1=0
So option (D) is correct.

Regards,

2 years ago

More Questions On Analytical Geometry

Post Question

Vouchers
To Win!!!
Q . IF THE DISTANCE OF ANY POINT ( x , y ) FROM THE ORIGIN IS DEFINED AS d( x,y) = max { | x | , | y | } , d( x,y) = a , non-zero constant, THEN THE LOCUS IS - A CIRCLE A SQUARE A STRAIGHT...

The answer, from the given options, should be A TRIANGLE. I got it by eliminating the rest of the options. P.S:- I have checked for the first three options. From them, i haven’t got the...

 Yash Jain 7 days ago
Tangents are drawn from the point (α,β) to the hyperbola 3x 2 -2y 2 =6 and are inclined at angles θ and φ to the x-axis. If tanθ.tanφ =2, prove that β 2...

 Sunil Raikwar 10 months ago

Hi Pranjal, There is slight technical issue. Please post these questions again in analytical Geometry. We will upload the answers for the same. askIITians Faculty

 sunil raikwar 10 months ago

Given equation is Equations of tangents are the roots of this equation is therefore Thanks &Regards, Sunil Raikwar, askIITians faculty.

 sunil raikwar 10 months ago
The equation of a straight line passing through the point (-5,4) and which cuts an intercept of root(2) units between the lines x+y+1=0 and x+y-1 is?

Hello Student. Please find the solutionx+y+1=0 and x+y-1 are two parallel lines and distance between them is mod|\frac{1-(-1)}{\sqrt{2}} |So distabce between them is 2/root2 = root2So our...

 Nishant Vora 2 months ago
The area of the triangle formed by the intersection of a line parallel to x-axis and passing through P (h, k) with the lines y = x and x + y = 2 is 4h^2. Find the locus of the point P.

Hello Student, Area of triangle=(1/2).AB.AC=4h^2 and AB= 2|k–1|=AC =>4h2 =(1/2).2.(k–1)^2 =>k-1 = ± 2h. =>locus is y = 2x + 1, y = – 2x + 1. Thanks &...

 Arun Kumar 5 months ago
a dice is rolled the probability of getting a number greater than 2 a odd number are they independent events if yes i cant see how practically

Ans: Hello Student, Please find answer to your question below Sample space, S is S = {1, 2, 3, 4, 5, 6} (i) Let E be the event of occuring a number on die greater than 2 E = {3, 4, 5, 6}...

 Jitender Singh one month ago

Two events are independent if the occurence of one event does not effect the probability of other. Lets say 1 st event to be A and 2 nd to be B. Let C to be intersection of A and B. A and B...

 Jitender Singh one month ago

no, i asked whether they are independent and how can this happen that the two events in single dice is independent

 rohan one month ago
evaluate the following integral ∫ 1 / sqrt(x) (sqrt(x) + 1) dx