Sign up to access problem solutions.

Already have an account? Log in here.

Explore how simple equations have graphical implications starting with the equation of a line.

Given that a straight line in the \(xy\)-plane passes through the point \((3,48)\) in the first quadrant and intersects the positive \(x\)- and \(y\)-axes at points \(P\) and \(Q\) respectively. Let \(O\) designate the origin.

Find the minimum value of \(OP\times OQ\).

Sign up to access problem solutions.

Already have an account? Log in here.

The line \(4x + y = 1\) passes through the point \(A(2,-7)\) and intersects point \(B\) on the line \(BC\) whose equation is \(3x - 4y + 1=0\). The equation of the line \(AC\) is \(ax + by + c = 0\) and constructed so that the distance from \(A\) to \(B\) is the same as the distance from \(A\) to \(C\).

What is the minimum positive value of \(a+b+c\)?

Note: \(A,B,C\) are all different points in the coordinate plane.

Sign up to access problem solutions.

Already have an account? Log in here.

Sign up to access problem solutions.

Already have an account? Log in here.

There exist two ordered triples \((a,b,c)\) for which \(4x^2-4xy+ay^2+bx+cy+1=0\) represents a pair of identical straight lines in \(x\)-\(y\) plane.

If these triples are \((a_1,b_1,c_1)\) and \((a_2,b_2,c_2)\), then find the value of \(a_1+b_1+c_1+a_2+b_2+c_2\).

Sign up to access problem solutions.

Already have an account? Log in here.

Given that a straight line in the \(xy\)-plane passes through the point \((3,48)\) in the first quadrant and intersects positive \(x\)- and \(y\)-axes at points \(P\) and \(Q\) respectively. Let \(O\) designate the origin.

Find the minimum value of \(OP+OQ\).

Sign up to access problem solutions.

Already have an account? Log in here.

×

Problem Loading...

Note Loading...

Set Loading...