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<\/a><\/p>\nBy this 5 questions, don\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2t assume that these same question are going to come (may be possible if I am very much lucky for you all), but yes the same concept will be helpful for sure. These questions are of good level and require good conceptual level.<\/p>\n
Let\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s start with the first question:<\/p>\n **For this type of questions, you should be strong in family of lines and properties of different quadrilaterals.<\/i><\/p>\n I Hope you understood all these very important questions in depth and also I am sure that now you will be able to solve many similar problems from this topic.<\/span><\/p>\n<\/div>\n I am Vijay Mukati,<\/a> Mathematics Expert at askIITians. I did my post-graduation from IIT Patna. For more about me you can visit the following link<\/span><\/p>\n You can also refer to some of my video lectures available on the following link<\/span><\/p>\n<\/a> How Should I Read this article<\/i><\/b>? If you are about to give JEE this year or next year, then I will suggest you to try solving this questions by your own. This will really help you in understanding your preparation for the exams and will give you the areas for the improvement. If you are not able to approach the question, then you can use the hints or steps given just after the question.<\/p>\n<\/a><\/p>\n<\/a> <\/a>(From the given combined equation of sides, find the equation of two sides by breaking it into linear factors. Here you will find, given fixed point will satisfy the one of the side of triangle. Since third side is variable through given point, find the limiting values of slopes by applying the appropriate conditions. Note that since the origin should be inside the triangle that means the third vertex of the triangle will be on the side of origin only.<\/i>)<\/p>\n<\/a>**If you were not able to approach this question, then you should focus on problems related to variable slope.<\/i><\/p>\n<\/a>(Given diagonal is member of both the families of lines, which means diagonal should pass through the common points of both the families (intersection points of L1<\/sub> and L2<\/sub>). You will find the given vertex is not satisfying this diagonal, so you can easily find the equation of other diagonal in point slope form (Diagonals of rhombus bisects each other and are perpendicular to each other). Find the intersection point of diagonals and using this, find the opposite vertex w.r.t given vertex.\u00c3\u201a\u00c2\u00a0 Then find length of this diagonal. Apply the formula for the area of rhombus in terms of diagonals. From here find the length of other diagonal.)<\/i><\/p>\n<\/a><\/p>\n<\/a>**For this type of problems you should also be strong in solution of triangles.<\/i><\/p>\n<\/a>(Whenever the pair of straight lines through origin is to be find, which are passing through the points of intersection of any curve and a line, always use the concept of homogenizing. Secondly if the pair of straight lines through origin are perpendicular then<\/i><\/p>\n<\/a>** Homogenation concept if very important. Please go through this concept if you have not studied till now.<\/i><\/p>\n<\/a><\/p>\n<\/a><\/p>\n